Maths-
General
Easy
Question
Kumar wants to spread a carpet on the floor of his classroom. The floor is a square
with an area of 4160.25 square feet. What is the length of carpet on each side?
Hint:
find the length of the side of the square by using the area of square formula in terms of length of side.
The correct answer is: 64.5 feet
Ans :- 64.5 feet
Explanation :-
Let the length of the classroom (square) be a cm .
The we get area of class room =
So we get , ![a squared equals 4160.25 not stretchy rightwards double arrow a equals square root of 4160.25 end root](data:image/png;base64,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)
We know that the length of side of square is length of the carpet to be used to cover it
I.e length of side of square = the required length of square carpet.
Using the long division method to find value of square root of 4160.25
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQQAAAIiCAYAAAAuFba8AAAgAElEQVR4nO3df1BU973/8df5ih7uNBccRtneq+v1BiNJlaYYNSZ6L0KilGsck2g1pTVqwdsbO2W5M9jMQMeMXpObhHYaTG/MdAnljuaXaSHqHSHYu6ij0OuvCv6YgghWiYp2t4K9XXDXed8/8uWdbHZBUHbPgq/HzM7Ecz67vvcHT3YPJ2KIiICICMD/s3oAIooeDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCFGora0NeXl5SExMhGEYqK2ttXqkQfP7/XjiiSeQn59v9Sh3raurC1/96ldhGIZeHnzwQavHCgsGIcps2bIF999/P9xuN/bu3Quv14v09HSrxxq08vJyuFwuq8cYEuXl5ejo6AjYtm7dOoumCa8Yqwegz+Xn5+Ptt99GTU0NFixYYPU4d6y5uRmvvvqq1WMMCY/Hgy1btsDn8yEmZuR/ufAdQpQoLS1FSUkJqqqqhnUM/H4/8vLy4HQ6rR5lSJSVlaG9vR2LFi3C/v37rR4n7BiEKNDa2oq1a9fC4XAMy48HX1ReXo7nnnsOkyZNsnqUu/bpp5/ixz/+MXp6elBTU4P58+dj7ty58Hg8Vo8WNgxCFCgrKwMAZGVlYdmyZYiNjUVsbCyKiorQ3d1t8XQD19zcjL1792L16tVWjzIkJkyYgD//+c9oa2uD0+lEfHw86urq8K1vfQt+v9/q8cJDyHI2m01M05SKigrxer3i9XqluLhYAEhGRobV4w2Iz+eTzMxMcbvdIiLS0tIiAMThcFg82dBxu92SkZEhAGT79u1WjxMWfIdgsfPnz6OjowM5OTl45pln9N1BQUEBsrKy4HK5UF9fb/WYt1VeXo4f/OAHSEhIsHqUsElISMBHH30Em82Gd955x+pxwoJBsNitW7cAAKNHjw7at2rVKgDA6dOnIzrTYDU3N+PUqVNYvHix1aOEXUJCAgoKCnDz5k2rRwkLBsFio0aN6nNfYmJiBCe5cwcOHEBJSUnAiTtTpkwBAN1eWlpq8ZRD55FHHrF6hLBhECw2efJkJCcno7q6us81NpstghMNXm5uLkQk4NLS0gIAcDgcEBHk5uZaPOXQuXr1KpYvX271GGHBIESBgoICNDU1BR0rOHnyJGw2G9LS0iyajL7M7/fj/fffx3e/+12rRwkLBiEKrF69GhkZGVixYgXa2toAAPv27cOPfvQjvP/++4iLi7N4wpHvwIED+qPeXj/72c+QmZmp73YuX76MVatW4aWXXhqxB09H/rmYw0BMTAw++eQTvPTSS0hNTUVnZydSU1NRX1+P1NRUq8e7Z82ZMwf//u//jgceeADx8fF4/vnn8cYbb2D8+PFWjxY2hgj/1WUi+gw/MhCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEKsbqAUYqwzCsHoFGMBEJy+0yCGEUrieNKFz4kYGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAiZUkQ2trakJeXh8TERBiGgdraWivGiGp+vx9PPPEE8vPzQ+6/ePEiSktL8eijj/a5xkq3e46vXbuGZcuWwTAMJCYmYu/evRZN2r+2tjZkZmbCMAwYhoHMzEy0tbX1ub60tFTX9l52794dwYnvkkRYSUmJAJDs7Gw5ceKEeL3eSI8QEXf70DqdTgEgDocjaF9LS4ukpqZKUlJSn2usdLvn2O12i91ul+LiYvH5fNLa2ip2u12cTqdFE4fW1NQkpmkKgICLaZrS1NQUtL6zszNovWma0tnZacH0dyaiQXA4HGKaptTU1ETyr7XE3QShqalpQF/sTU1NUReEgTzHOTk5Mnfu3IBtu3btEtM0pb29PdwjDlhOTo44nU7p6uoSEZGzZ8/KjBkzBIAsWbIkaH1xcbF88MEHkR5zSEUsCL3f8VwuV6T+SkvdaRB8Pp9kZmaKy+W67Rd7S0tLVAVhIM9xe3u7AJCtW7cGbO/s7BQAUlJSEu4xByzULG63WwBISkpK0HbTNGXChAmyefNmuXr1aqTGHFIROYbQ2tqKtWvXwuFwID09PRJ/5bBVXl6O5557DpMmTbJ6lEEZ6HN88OBBAEBycnLA9ri4OMyePRsff/xxWOccjLy8vKBtCQkJmD17NsaNGxew/ec//zl6enrw6aef4sc//jHsdjs+/PDDSI06ZCIShLKyMgBAVlYWli1bhtjYWMTGxqKoqAjd3d2RGGFYaG5uxt69e7F69WqrRxm0gT7HTU1NABAyeKNHj476A8xdXV04fPgwcnJyArZv2LABf/rTn/A///M/eOqpp9DT04Pnnnsu6u9PkEi8DbHZbGKaplRUVIjX6xWv1yvFxcUCQDIyMiIxQsQN9qHt/ajgdrtFZGAfB6LpI8NAn2OHwyEApKWlJeg25s6de9cHY8Ntz549Yrfbxefz9btu165dAkBsNttt10aTsD/6bW1tAkDWrVsXtC8rK0sASF1dXbjHiLjBvrCdTqfs2rVL/zycgjCY53g4B8Hn80lKSoocPnx4QOu3bt0qAGT//v1hnmzohP0jw61btwB89nbwy1atWgUAOH36dLjHiGrNzc04deoUFi9ebPUod2Qwz3FCQkLkBhtib7zxBvLy8jBr1qwBrc/Ozgbw+eMzHIQ9CKNGjepzX2JiYrj/+mHhwIEDKCkpCTiZZcqUKQCg20tLSy2esm+DeY57DyZ6PJ6gtS0tLVF70Ln3WEBubu6ArxMXF4e5c+eGa6SwCHsQJk+ejOTkZFRXV/e5xmazhXuMqJabmwv57OObXlpaWgAADocDIjKoF2KkDeY5njdvHgCgoaEhYH9HRwc6Ojrw9NNPh2/QO1RbW4udO3eioKAgYPuNGzdue90LFy7gkUceCddoQy4iP2UoKChAU1MT6uvrA7afPHkSNpsNaWlpkRiDwmigz/GECROQk5ODioqKgHV1dXUwTRNLly6N2MwDUV9fj48++gg/+clPArb/9re/xfbt2/u97t69e1FYWIi4uLhwjji0InGgwufzSUZGhtjtdmltbRURkdraWjFNc8SeqHS3D+1ADhgeOXJEAMjatWstP5I9mOe4vb1d4uPj9eSkxsZGsdvtsm3btojP3Wv//v1imqYUFhbqNpfLFfLU5d5LQ0ODiIhcuXJFHnroIXE6neL1esXn80lVVZW88MILlj8vgxWxQ7o+n08KCwslPj5eAEhqaqocP348Un99xIU7CKFeoFbHdTDP8YULFyQtLU0AyLRp0yw/nf3LQTh27FifIQAgycnJel2fzyerV6/WfampqVJVVWXVXbkrhgh/vVA4GIbB39xEww7/PQQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgRJEzZ85g/vz5MAwDsbGxKCoqgt/v7/c63d3dKC0txZQpU2AYBvLz8yM0LY1EMVYPQJ9pbm7Gu+++i927d+Ov/uqv8Jvf/AZPP/00/vd//xdvvPFGyOv87ne/Q3p6OsaNG4f/+I//wKOPPoqxY8dGeHIaUYTCYrAPrdPpDNr26quv9nk7LpdLAMj69evF5/Pd0YxEX8Z3CFFi9erVQdvi4+Nht9uDtjc3NyMrKwsOhwOvv/56JMaje4QhImL1ECORYRi4m4e2u7sbU6dOxX/+538iPT09YN+8efPQ0tKC5uZmxMXF3e2oRIoHFaOM3+/H/v37MX36dLz11ltBMaivr8ehQ4fwr//6r3jzzTeRmJgIwzAwf/58tLW1WTQ1jRQMQpSZP38+5s+fj3PnzuG73/0u6uvrA/bv3bsXAOB2u/G9730PV69eRX19PX7729/ioYceQmtrqxVj0wjBIESZgwcP4k9/+hMKCwvR2dmJ9PT0gC/yffv2AQBeeeUV/M3f/A0AYM6cOXjnnXfQ09ODsrIyS+amkYFBiEJjx47Fyy+/jK1bt6Knpwc1NTW67+bNmwCAmJjA48FPPvkkgM+DQXQnGIQolp2dDQD4/e9/r9vGjBkTcq3NZovITDSyMQhRrPcnCA8//LBu+6d/+icAQGNjY8jr3H///eEfjEYsBiGKNTY2wjRNLFmyRLc9++yzAIAdO3YErD1z5gwAYM2aNZEbkEYei0+MGrEG89BeuXJFTNOUp556Ss6ePSsiImfPnpVp06aJy+UKWu90OgWAVFRUiIjIpUuXZMaMGeJwOIZmeLpnMQhhMpgg+Hw+Wb16tQAQADJ+/Hj54Q9/KK2trX1ep6amRiZMmKDrQ536TDRYPFMxTO72TEUiK/AYAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkYu7myoZhDNUcIxIfHwoXEQnL7d5VEMI11EhgGAYfHxp2+JGBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIhWxIPj9fjQ0NKCwsBATJ05EbW1tyHXd3d0oKirC2LFjYRgGJk6ciOrq6tvevsfjwaRJk1BaWjrUo0dUa2srDMMIuDz//PNWjzVobW1tyMvLQ2JiIgzDCHq+r127hmXLlsEwDCQmJmLv3r0WTUoBJELKyspk4cKFYpqmABCXyxW0xufzSUZGhgAIujidzn5v3+FwDGhdpNzpQ5uTkxN03/fs2TPE04VXSUmJAJDs7Gw5ceKEeL3egP1ut1vsdrsUFxeLz+eT1tZWsdvtUfPc3csiFoReW7du7TMIe/bskeXLl8uFCxdERKSrq0vWr1+vXxhXrlwJeZsul0vsdvuwD0JDQ4MsWbIkDNNEjsPhENM0paamps81OTk5Mnfu3IBtu3btEtM0pb29PdwjUj8iHgSn09lnEN566y3x+XxB21esWCEA5NSpU0H73G63zJkzR3bt2jXsg7By5UqJj4+XpUuXhryv0a6/57ZXe3u7AJCtW7cGbO/s7BQAUlJSEu4xqR9RdVDxhRdeQExM8D/RMH/+fADAV77ylaB9mzZtwmuvvYb77rsv7POF05EjR7Bt2zZ0dnbi17/+NaZPn47vfOc78Pv9Vo82IK2trVi7di0cDgfS09P7XHfw4EEAQHJycsD2uLg4zJ49Gx9//HFY56T+RVUQ+lJXV4esrCxMnjw5YHttbS0SEhLwj//4jxZNNnRmzZoFr9eL3//+99i8eTNM08R7772HgoICq0cbkLKyMgBAVlYWli1bhtjYWMTGxqKoqAjd3d26rqmpCQAwadKkoNsYPXp0nwebKTKiPghdXV3YsWMHNm7cGLDd4/HgtddeQ2FhoUWTDb3Y2FgkJyejqKgIZ8+ehd1uR0lJCerr660e7bZKS0thmib+8pe/YPv27bh+/To2b96MV155BYsWLdJ1Ho/HwinpdqI+CL/4xS9QWFiIWbNmBWzftGkTXn/99ZAfMUYCu92O3/zmNwCAyspKi6fp3/nz59HR0YGcnBw888wz+u6goKAAWVlZcLlcwyJqFOVBaGxsRFVVVdC7gNraWjz44IP4+te/btFkkTF16lSsXLkSN2/etHqUft26dQvAZ2/5v2zVqlUAgNOnTwMAEhISIjcYDVrUBqH3I8FHH30U9C5g586deOGFFwJO3snIyAAArF27NuSJMMPVcDg+MmrUqD73JSYmBvy592BiqI8OLS0t/R6QpPCLyiB4PB4sWrQIb775ZsB3lBs3bgAA3njjDchnPzLVi8vlAgA4nU6IyIh5YV26dAmZmZlWj9GvyZMnIzk5ud8zSm02GwBg3rx5AICGhoaA/R0dHejo6MDTTz8dvkHptqIuCB6PB6tWrcKOHTsCYnD58mW8+OKLFk4WeR6PB8ePH8eCBQusHuW2CgoK0NTUFHSs4OTJk7DZbEhLSwMATJgwATk5OaioqAhYV1dXB9M0sXTp0ojNTCFE+sSHTZs2CQDZvXt30D632y1JSUkhT10GIMXFxX3ersvlGtYnJv3zP/+zrF69Wi5duiQiImfPnpWnnnpKz9qMdr2nndvtdmltbRURkdraWjFNM+hEpfb2domPj9eTkxobG8Vut8u2bdsiPjcFilgQer9gv3z5ot7Tj/u6NDQ03Pb2h2sQPvjgA4mPjxcAMn78eNm8eXPQ/wMQ7Xw+nxQWFur9SE1NlePHj4dce+HCBUlLSxMAMm3atH5PdabIMUT464XCgb+5iYajqDuGQETWYRCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDEKU8vv9eOKJJ5Cfn2/1KAPm8XiwZs0axMbGwjAMZGZm4uLFi/1ex+/3o7KyEo8++igMw8C8efMiNC2FwiBEqfLycrhcLqvHGDCPx4NvfOMb+Pu//3tcv34dXq8XdrsdDzzwAJqbm0Ne5+LFi3jwwQexZs0aOBwOXLt2DQcPHozw5PRFDEIUam5uxquvvmr1GIPy85//HGPHjsWGDRsQGxuL2NhYvP3225g6dSq+973vBa1vbm7GAw88gClTpuDKlSvIzs7GuHHjLJicvohBiDJ+vx95eXlwOp1WjzJgfr8fr7zyCjIyMgK2x8TEIC8vD4cOHcKRI0d0u8fjwZNPPom5c+fiv/7rvxAbGxvpkakPDEKUKS8vx3PPPYdJkyZZPcqA/eEPf0BPT0/IfUlJSQCAhoYG3bZp0yZcvHgRTqcTMTExEZmRBoZBiCLNzc3Yu3cvVq9ebfUod+T8+fO3XfPpp5+ipKQEK1euRH19PSZOnAjDMDB9+nQcPXo0AlNSfxiEKNH7UWHr1q1WjzJoSUlJsNls2LlzJz799NN+1/YeNOzp6cGjjz6K9vZ2nD17Fl1dXZg1axYOHDgQiZGpDwxClCgvL8cPfvADJCQkWD3KHSkpKQEAPP/887h8+TIAoKmpSbf3fnQ4duwYAODf/u3fMGXKFADAlClT8OGHHwLAsDuYOtIwCFGgubkZp06dwuLFi60e5Y6tWLECNTU1OHnyJP72b/8W06dPR1tbG27evAnTNPHII48AAG7evAkAGDVqVMD1H3vsMdhsNlRVVUV8dvocgxAFDhw4gJKSEhiGoZfe756920tLSy2e8vYWLFiAq1evQkRw6tQpTJ06FVVVVdi8eTPi4uIAAGPGjOnz+r33mazDIESB3NxciEjApaWlBQDgcDggIsjNzbV4ysHx+/1Yu3Yt7HZ7wNmW//AP/wAAOHPmTMjrJScnR2Q+Co1BoCHX3d2N73znOzh79iwOHToU8KPFtLQ02Gy2oIOnXV1dOHr0KAoKCiI9Ln0Bg0BD5vr166isrMT06dPR3t6OY8eOwW63B6yJi4vD+++/j6qqKvzkJz+B3+/HjRs3sHbtWsydO3fY/sh1pGAQaEjMmzcPX/3qV/H222/jnXfewaFDhzB+/PiQa9PT03H8+HG89957GD16NOx2O6ZMmYJPPvmEJypZzBARsXqIkcgwDPChpeGG7xCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIhVzN1c2DGOo5hiR+PhQuIhIWG73roIQrqFGAsMw+PjQsMOPDESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhGpiAXB7/ejoaEBhYWFmDhxImpra0Ou6+7uRlFREcaOHQvDMDBx4kRUV1eHXNvW1obMzEwYhgHDMDBjxgwcPXq0zxnmzZuna3svXV1dQ3L/KFBbWxvy8vKQmJgIwzD6fL4BoLa2FoZh4Ny5cxGcMNjRo0cxY8YMGIaB2NhYrFmzBteuXetzfX5+ftDrqbGxMYITh4FESFlZmSxcuFBM0xQA4nK5gtb4fD7JyMgQAEEXp9MZsPbcuXNimqYUFxeL1+sVEZGKigoBIPv37w+67T179gTdZk5OTnjurIhE8KGNOiUlJQJAsrOz5cSJE/r8hOJ2u8VutwsAaWlpieCUgVwuV8jXnd1uF7fbHbT+9OnTQWtTUlIsmHxoRfxVu3Xr1j6DsGfPHlm+fLlcuHBBRES6urpk/fr1+oBfuXJF127cuFFmz54ddBvr1q2TJUuWBGzz+Xwyc+ZMaW9vH+J707d7NQgOh0NM05SampoBr4+GIMycOVOqqqo0XvX19TrXxo0bg9avXLlSDh8+HOkxwy7ixxBiYvr+P67Pnz+Pd999F3a7HQDw13/913j99dexYsUKAMAf//hHXevxeNDZ2Rl0G6NHjw7aVlVVhaNHj+LZZ59FZWUl/H7/3d4NCqG0tBQlJSWoqqrCggULbru+trYWY8aMwbPPPhuB6fp2/vx5bNiwAd/85jcRGxsLAJgzZw527twJALhw4ULA+sbGRmzbtg3f/va3UVpaiu7u7ojPHDaRLpDT6ezzHUJfet9VtLW16bbet6Vf/Cjh8/kkJSUl4LuTz+fT0vdekpKSpKmpaWjuUB8seGgtde7cOQEgDodjQOvdbrfMmTNHOjs7xeFwWP4OIRSfzycAZP369QHblyxZEvB6io+Pl7q6OoumHFrDIggrV66UrKysgG2dnZ36hV5SUiJer1dycnLkgw8+CHkbly9flnfffVeSkpL6/Ww4VO61IBQVFQkAqa6ulqVLl4ppmmKaphQWFoY8huBwOPQtd7QGoaGhQQCE/GK/du2aVFdXy+OPPy4AxDTNsH+TiYSoD0JnZ6eYphny85rb7dYv8Pj4eDlx4sRtb8/n80lOTo4AkKKiokHPP1D3WhBsNpuYpikVFRXi9XrF6/VKcXGxAJCMjIyAtS6XS4qLi/XP0RqEkpKSoONRofTezy9/0xqOoj4IxcXFIQ/q9NqyZYukpaVpFI4fP37b2/T5fDJ37lwxTXPAcw/WvRSEtrY2ASDr1q0L2peVlRXwXdbtdktmZqb4fD5dE41BcLvdEh8fP+AD0evWrQv6WDscRfWJSY2NjaiqqkJhYWHQPr/fj9zcXIwePRr79u1DRUUFuru78dhjj+HIkSP93m5MTAxefPFF9PT0hGv0e8qtW7cAhD6gu2rVKgDA6dOnAQCbNm3Cli1b+j24HA3y8/NRWVmJCRMmDGj997//fQCfPxbDVqQLNNB3CG63W7Kzs/v8nN97ULGzs1O3nT59WkzTHNDPg1taWsL6XdyCh9Yyve8QQh1Q7P35fu/BX4T4Wf+XL1ZzOp2ya9euQV8PUfYu505E5TsEj8eDRYsW4c0330RCQoJuv3Hjhv73jh078PDDDyMuLk63fe1rX8P777+PkydP3vasN4/Hg5ycnKEf/h40efJkJCcn93lGKQDYbDYAn/1L3V++OBwOAEBLS4vl/1J1aWkpAGDx4sUB27/42gulo6MDKSkpSEpKCttskRB1QfB4PFi1ahV27NgREIPLly/jxRdf1D+PGTMGDQ0N8Hg8Ade/7777YJomxo8f3+/fU15ejh/96EdDO/w9rKCgAE1NTaivrw/YfvLkSdhsNqSlpVk02cB9+OGHuH79OnJzc3Wb3+9HZWUlDh482O91Kysr8dOf/jTcI4ZfpN+SbNq0SQDI7t27g/Z98acGoS5fPDK9f/9+ASDLly+XS5cuiYjI2bNnxW63B5ybUFlZKbNnz5b6+noR+fzsxzt5SzgYFjy0luo97dxut0tra6uIiNTW1oppmrf9eBgNBxV/+ctf9vsxpvej6bFjx+Shhx6Sqqoq8fl84vV6xel0Brw2h7OIvWr7Olf8i758AtGXLw0NDQHrjxw5IgsXLtT9qampUlVVFbCmqalJpk2bpj8rXrp0qb5gw+leC4LIZ1EoLCyU+Ph4fT4G8lMfq4Pwq1/9qt/X3cqVK3Wt2+3Wn2oBkIULF8qRI0csmTscDBH+eqFw4G9uouEo6o4hEJF1GAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUjZzYWQAAAo5SURBVAwCESkGgYgUg0BEikGgsGhra0NeXh4SExNhGAZqa2v7XFtbWwvDMHDu3LkIThjs6NGjmDFjBgzDQGxsLNasWYNr1671uT4/Px+GYQRcGhsbIzhxGAiFxb380JaUlAgAyc7OlhMnTojX6+1zrdvtFrvdLgCkpaUlglMGcrlcAiDoYrfbxe12B60/ffp00NqUlBQLJh9a9+6rNszu1SA4HA4xTVNqamoGvD4agjBz5kypqqrSeNXX1+tcGzduDFq/cuVKOXz4cKTHDDt+ZKAhU1paipKSElRVVWHBggW3XV9bW4sxY8bg2WefjcB0fTt//jw2bNiAb37zm4iNjQUAzJkzBzt37gQAXLhwIWB9Y2Mjtm3bhm9/+9soLS1Fd3d3xGcOG6uLNFLdaw/tuXPnBIA4HI4BrXe73TJnzhzp7OwUh8Nh+TuEUHw+nwCQ9evXB2xfsmRJwEeF+Ph4qaurs2jKocV3CDQkysrKAABZWVlYtmwZYmNjERsbi6KiopDfQTdt2oQtW7YgLi4u0qMO2JkzZwAAzzzzTMD2jz/+GNeuXUN1dTUef/xxdHZ2Ij09Hc3NzVaMOaQYBBoSpaWlME0Tf/nLX7B9+3Zcv34dmzdvxiuvvIJFixYFrK2trcXEiRMxa9Ysi6YdmH379mHJkiV47LHHgvaNGzcOmZmZOHToEIqLi9HT04P8/HwLphxiVr9FGanupYe2ra1NAMi6deuC9mVlZQkAfUvtdrslMzNTfD6fronGjwxut1vi4+Olvb19QOvXrVsnAKStrS3Mk4UX3yHQXbt16xYAYPTo0UH7Vq1aBQA4ffo0gM8/KsTExERuwDuQn5+PyspKTJgwYUDrv//97wP4/LEYrqL7WaFhYdSoUX3uS0xMDPhzSUkJSkpKQq6dMmUKAEBEhm64O1BaWopvfetbSE9PH/B1vv71r4dxosjhOwS6a5MnT0ZycjKqq6v7XGOz2QB89sX+5YvD4QAAtLS0REUMAGDx4sUB22/cuNHv9To6OpCSkoKkpKSwzRYJDAINiYKCAjQ1NaG+vj5g+8mTJ2Gz2ZCWlmbRZAP34Ycf4vr168jNzdVtfr8flZWVOHjwYL/XraysxE9/+tNwjxh+Fh6/GNHutYfW5/NJRkaG2O12aW1tFRGR2tpaMU1TXC5Xv9eNhoOKv/zlL0Oeutx76ezsFBGRY8eOyUMPPSRVVVXi8/nE6/WK0+mU4uJiy2YfSjyGQEMiJiYGn3zyCV566SWkpqais7MTqampqK+vR2pqqtXj9evXv/411qxZ0+f+lStX6vkSkydPRmJiIrKysgAACxcuxMsvv4yZM2dGZNZwM0Qs/tA2QhmGYfnnYaLB4jEEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEjF3M2VDcMYqjlGJD4+FC4iEpbbvasghGuokcAwDD4+NOzwIwMRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEKmJB8Pv9aGhoQGFhISZOnIja2tqQ67q7u1FUVISxY8fCMAxMnDgR1dXVIddevHgRmZmZMAwDsbGxWLNmDTweT8i1Z86cwfz582EYBqZPn47f/e53Q3bfaOSoqKhAYmIiDMPo9/U0YkmElJWVycKFC8U0TQEgLpcraI3P55OMjAwBEHRxOp0Ba5uamsQ0Tdm+fbv4fD65evWqZGRkiN1uF7fbHXJtRUWFiIgcOXJETNMMOcNQieBDS0PE6XSK3W6X1tZW8fl8UlxcHPL1NJJF/FW7devWPoOwZ88eWb58uVy4cEFERLq6umT9+vUahStXrujaJUuWSE5OTsD13W63mKYpDocjYHtKSkrQtt4n2+fzDdVdC8AgDC+nT58Oel36fD5JSUmRjRs3WjhZZEX8Vet0OvsMwltvvRXyC3TFihUCQE6dOiUiIufOnQv5rkFExOFwBMSjrq5OAEhNTU3AuoaGBgEge/bsGYq7FYRBGF6KiooEQNDrr7i4WEzTlM7OTosmi6yoOqj4wgsvICYm+J9omD9/PgDgK1/5CgDgD3/4Q5+3MX36dACfHTMAgL179wIA7r///oB1X/va1wCgz2MZdG8pLS3F3Llzg15/Dz/8MHp6enDixAmLJousqApCX+rq6pCVlYXJkycHbL906dJtr3v8+HEAQFJSUsD23ie+rq5uiKak4aqjowMdHR2YOXNm0L7e10lzc3Okx7JE1Aehq6sLO3bswMaNG3Vb73f3t956C36/v9/r//GPfwzrfDT8/fnPf7Z6hKgR9UH4xS9+gcLCQsyaNUu32Ww2bNy4ER0dHfiXf/kX3LhxQ3+suWXLFgDA3/3d31k1MtGwFdVBaGxsRFVVFQoLC4P2bdiwAU6nE7/61a8QFxeHJ598El6vF1evXkVKSooeMxg3blykx6Zh5r777rN6hKgRtUHweDx47bXX8NFHH4U80AgAubm5uH79OkQE+/btg9frRUdHB15++WVdM2PGDACffU78ot4/P/7442G6BzRc2Gw22Gw2nD9/Pmjf1atXAQBTp06N9FiWiMogeDweLFq0CG+++SYSEhJ0+40bN/q9zqpVq7BkyRIsXrxYty9YsADA5z916HXhwgUAQHp6+lCOTsNUbm4uqqurg45JNTU1wTRNfOMb37BossiKuiD0fmHv2LEjIAaXL1/Giy++GPI6165dw4IFC/DAAw+grKwsYN9jjz2GlJQU/Pd//3fAdpfLBbvdrsGge1t2djZ6enpw5MgR3eb3+/Hee++hsLAQcXFxFk4XQZE+8WHTpk0CQHbv3h20z+12S1JSUshTlwFIcXFxwPpr166J0+mU+Ph4yc7OFq/XG/LvPHz4sJimqScn1dbWSnx8vOzfv3/o7+D/Z8FDS3dp8+bNYrfb5erVq+L1emXjxo2SlJR0z5yUJBLBMxVdLlfIL/IvstvtfcYAgDQ0NHw+OCDx8fGydOlSPYOxP8ePH5dp06YJAElLS5Pjx48P+X38IgZheOr9BmOapvzwhz+8p/4/BhERQ4S/Xigc+JubaDiKumMIRGQdBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJFiEIhIMQhEpBgEIlIMAhEpBoGIFINARIpBICLFIBCRYhCISDEIRKQYBCJSDAIRKQaBiBSDQESKQSAixSAQkWIQiEgxCESkGIQwERGrRyAaNAaBiBSDQESKQSAixSAQkWIQiEgxCESkGAQiUgwCESkGgYgUg0BEikEgIsUgEJH6P+eZEiy0z/oBAAAAAElFTkSuQmCC)
![a equals square root of 4160.25 end root equals 64.5 text (feet) end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMwAAAATCAYAAADcSuIIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABG1JREFUeNrtWl1IFFEUHmQRCYmCRKJiI0QkQoRaSkxCCImIEFFKfDQkQkJ6Cmyh6CHpoaIgkAqJqIcwixALQiIkxBCTiIhCIkJEBAMRk2VrOzc/YZzu/8y4uzgffJQzZ2fvOfeec79zdxwnN1FMzERcxQgRhDhJfB2FIUIEPbwgnorCsO5whtidxe/vxhjyCluIP/FvhPWDSuJIDozjLcaSNzhNfKphd0yh7cuJSeKE4jkJ4mPiPHGJ+Jx4yGOzkXibOAr24JoINcQ+PDOFMbRy7LLZs+j4bRJvv/6whVrluXaEOElMr2Eft5c4nE8Jw3qXJo1DgU+KID4gtits2rFQyl2J0coJ2BDxuGfxDEme+4bYgnEy7MaCaOEssGxA12+TePvxpwrx8eI7YhcG5iT3hpE4OY+dxFlikcKOVfg2zQkS2bCJGNP4fDPxJuf6DU4CyBAnfsiBhNH12ybetv5cJXYE+DzHx7pgOKvTSxUQLxFnXDIivsaTeZ54R2FT46rufhKmR3PBM2lVz7leh3smWMqBhOkxTHSTeNv685JYq5B3brDx/0A8ewUFVmajkovVCgXxDwOopJuRPEzfNljqVVsd/h66VYRCVOl4AAnzmbhVc+suFIxlxsC3ao7s8JMwtvHX9dsm3rb+zAtizHvefviwA+uUyctrFjYZhd/zsgG3IEHcuE88GlKVK+Zc20OcJsYkn+v2bN1+EmYJGr6fuIhddYzTnKclz05p+luEw4IazthSmJxB4jlBbIKErt828bb1J20wd/2cHXLawkblS0rVaFdzGtegJVkZtkc22IOee1eI1yWfrbSs0BnJ9XEUhRgqEVvQX5zVZ/FpA4nFA9uxnwlk3QpiaDKTqIwVIWt3Hb9t423jj0nCLBBLOTuUqY2vhFlE4Nz9zEIIkuACEob9zvLOc+8bcZ/k+0aRcEElDAvgNsGJzZTr7xmBXCjSkGS7kCxlBgu6HsUqLEmm67dtvG38MZFkOr7q2lhLsllOozceYpVjleyPqwocIH5VyDHbfkl0b9BTJETVpU/QV9Urmv4KHGBssJRNYUHX7yD7U5U/rzhyVTR3cxox1bHJKPpNadM/5TlFSFqcAJmC7WqP8P9bxIsBHw2qbFjSnhAs9FHX342Ck7teyWlTKXrCmIVPrJebDLlY6fgdVFOv44/JsTKLe5vieTo2KUnh6MCYhLjsLB83FqBveYhKFCbuEn9hUc1a6nY/CVMIqdDmWtj7cSp0mNPjdcKOfa6LIzPclXdA059+VLMCcOWX7cYQ427it4lE8uOP6IfLjKAPnnT1hHEcUJnaTEgKntYPl12oikmXPm8IceI2EX8Tnzj27xCppJhKRpRg91hA48kWUq2gcb8HabGI4lIsWTi6UqYZzXYaMoLFP+GED12/TRPGjz8jzv/vcInmN4EEY9/z0Vn9FoauTR3WuPc7rF+NKVmDiRvGgDudCOsd0cuXGkggYbZH6yWCs/zibTZf72d9S3uuB6kpWicR8gV/AR068fM7GVpeAAAAqnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5hPC9taT48bW8+PTwvbW8+PG1zcXJ0Pjxtbj40MTYwLjI1PC9tbj48L21zcXJ0Pjxtbz49PC9tbz48bW4+NjQuNTwvbW4+PG10ZXh0PiYjeEEwOyhmZWV0KSYjeEEwOzwvbXRleHQ+PC9tYXRoPiyRa4QAAAAASUVORK5CYII=)
The length of carpet be on each side is
.
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Maths-
In the given figure, PQ || RS. Check whether ΔPOQ i congruent to ΔSOR Give reason for your answer:
![](data:image/png;base64,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)
In the given figure, PQ || RS. Check whether ΔPOQ i congruent to ΔSOR Give reason for your answer:
![](data:image/png;base64,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)
Maths-General
Maths-
Show that 64 is square as well as cube number
Show that 64 is square as well as cube number
Maths-General
Maths-
From the given figures, find by which criteria the two triangles ABC and PQR are congruent.
In the figure XY = PZ. Prove that XZ = PY.
In the figure XY = PZ. Prove that XZ = PY.
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)
From the given figures, find by which criteria the two triangles ABC and PQR are congruent.
In the figure XY = PZ. Prove that XZ = PY.
In the figure XY = PZ. Prove that XZ = PY.
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)
Maths-General
Maths-
Evaluate: ![cube root of 3375](data:image/png;base64,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)
Evaluate: ![cube root of 3375](data:image/png;base64,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)
Maths-General
Maths-
Evaluate: ![cube root of fraction numerator left parenthesis negative 1728 right parenthesis over denominator 2744 end fraction end root](data:image/png;base64,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)
Evaluate: ![cube root of fraction numerator left parenthesis negative 1728 right parenthesis over denominator 2744 end fraction end root](data:image/png;base64,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)
Maths-General
Maths-
In the figure above,
and BC = XZ. What additional information is required to make ABC ⩭ YXZ by RHS congruence condition?
![](data:image/png;base64,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)
In the figure above,
and BC = XZ. What additional information is required to make ABC ⩭ YXZ by RHS congruence condition?
![](data:image/png;base64,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)
Maths-General
Maths-
Find the square-root of the following numbers.
b) 25921
Find the square-root of the following numbers.
b) 25921
Maths-General
Maths-
In the figure, AF is perpendicular to BC and AF is the angle bisector of
, then state the rule used for the congruence of Δ DAF an ΔEAF.
![](data:image/png;base64,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)
In the figure, AF is perpendicular to BC and AF is the angle bisector of
, then state the rule used for the congruence of Δ DAF an ΔEAF.
![](data:image/png;base64,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)
Maths-General
Maths-
Find the least number by which 85750 must be divided so that the quotient is a perfect cube?
Find the least number by which 85750 must be divided so that the quotient is a perfect cube?
Maths-General
Maths-
In the figure, ABC is an isosceles triangle with AB = AC. If D is the midpoint of BC, prove that:
(i) ΔABD⩭ ΔACD
(ii)
90°
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)
In the figure, ABC is an isosceles triangle with AB = AC. If D is the midpoint of BC, prove that:
(i) ΔABD⩭ ΔACD
(ii)
90°
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)
Maths-General