Maths-
General
Easy
Question
Simplify √12 - √48 +√1323
Hint:
Use prime factorization.
The correct answer is: 19√3
Complete step by step solution:
On prime factorization, we can write
![square root of 12 equals square root of 2 cross times 2 cross times 3 end root comma square root of 48 equals square root of 2 cross times 2 cross times 2 cross times 2 cross times 3 end root](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUUAAAATCAYAAAAH1B8DAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA4tJREFUeNrtXE1IFVEUvkiIiIuiQKLAEImIkKCCwiTcRIiLhxgULSKKkIhoGVTQJnIRFLWKihZRQfS3iAoiJCLCFhUREka0aOHCRSBSg1D2Hd6xXsPMvHtvM2fGN+eDD/XNZc7P/Thz75nrM8YebeCcACUhFdNC40LIqepEmbu2doGjprHQiDFpTjUmhRAegwc0JoXqRKEwZhn4jX9qTArViaL0GAbvJ1xfDZ4E38Vc7wHvgNPgLI/bU9CYJH2VtNUHPgK/gwE4AZ4HlwrqZB4DJr530wpeAGfYzyfgCtWJ2iqa/qmfMpRw/Tp4MEHoz8HdptqwJqwFX/JneSEuJklfJW1RvINgc81n67noZJ3TWlCs4wlauQqeBhexryPgmOpEbRVJ/6vAKbDFYqzLm5sO8H1OQneJSdpX6bxMC+f0Erg/QStB6O8mXkWoTtRWYfR/DLxsOdb1qESQk9hdYrLx9TjT9VretjrBj4I5pe3SszpamalZOcwXxa+qE7VVJP2/BXdkUBS38FLZ5p5pn1lzicnW16gJ8RGEhK12cB/3VfpTKiD1ctrMK4COOlqhfuKRUD7Oqk7UVh76b4v4bB04yf2dNItiC/eJejJ+0qcRk4uvtRPjI4isbYWLxFHBnFJv8LCFVrp5uzzLPSe6b6/qRG1J6r8LvMaDtoaunQHPOQRlUxSXgA/A7RmKPK2YfHylyXnqIQhpWxUW4DaBnHZHPP3nYvpJN8Dl5m9DfAP4me+hOlFbIvo/wcKgs1ivQ9e+gBtTLIqdHHiX4z1dt0VpxOTjq+9ESdoKr5Bs3+z+T07HImKLmrd7McWPjlOMqk7UlrT+D4G/eL9N2Ax+ctg+1CuKa0y1ad1q5OAbk6+vPkt6SVtRCARyalusghT9VJ2orVT0Twcbb/LvF8FTjgbiiiKJ7bZjgU0LrjH5+urT/JW0FbetnRDIqa1WxmNWC3R+bVJ1orby0P8V8Ac7OcVVPI2i+NDjXmnBNSYfX32PCUjaopcWOzkPTbwlpS3i3pjxt3g+KxnoJE4rg1wY+9jHeT+ppzisOlFbgvr/g8XgT/Au+MpR4En9mzy/Aso1JklfJW31sggDJvXoBhLGJxVFX53YPEBJuG9M9e1zwGKuqE7UlrD+/8EL439co6hoxJgkQIWxX3WiKDs2sTBWakylBv1f6IeEfo/qRFEqDGlMpQd9M0276kRRNvwGPbwFiV4zMtsAAAFZdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zcXJ0Pjxtbj4xMjwvbW4+PC9tc3FydD48bW8+PTwvbW8+PG1zcXJ0Pjxtbj4yPC9tbj48bW8+JiN4RDc7PC9tbz48bW4+MjwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1uPjM8L21uPjwvbXNxcnQ+PG1vPiw8L21vPjxtc3FydD48bW4+NDg8L21uPjwvbXNxcnQ+PG1vPj08L21vPjxtc3FydD48bW4+MjwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1uPjI8L21uPjxtbz4mI3hENzs8L21vPjxtbj4yPC9tbj48bW8+JiN4RDc7PC9tbz48bW4+MjwvbW4+PG1vPiYjeEQ3OzwvbW8+PG1uPjM8L21uPjwvbXNxcnQ+PC9tYXRoPmyK3yMAAAAASUVORK5CYII=)
and ![square root of 1323 equals square root of 7 cross times 7 cross times 3 cross times 3 cross times 3 end root](data:image/png;base64,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)
This can be written as
and
respectively.
So, ![square root of 12 minus square root of 48 plus square root of 1323 equals 2 square root of 3 minus 4 square root of 3 plus 21 square root of 3 equals 19 square root of 3](data:image/png;base64,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)
Related Questions to study
Maths-
In
, the bisectors of
and
intersect each other at O. Prove that
![90 to the power of ring operator plus 1 half straight angle A](data:image/png;base64,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)
In
, the bisectors of
and
intersect each other at O. Prove that
![90 to the power of ring operator plus 1 half straight angle A](data:image/png;base64,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)
Maths-General
Maths-
and are the medians of a
right angled at . Prove that
.
and are the medians of a
right angled at . Prove that
.
Maths-General
Maths-
In
right angled at A, AL is drawn perpendicular to BC. Prove that
.
![](data:image/png;base64,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)
In
right angled at A, AL is drawn perpendicular to BC. Prove that
.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAO0AAACUCAYAAAB/YK6GAAAc5ElEQVR4nO3deVxVdf7H8de5C3CVRVAxJE1cUktFRNNQcRulyUZ9pISAQpKIK2rqoNk0lVnUI0eThkUBEUVxZNKgRVP7jfOzSckFE8F1LE2ZNDYVBe695/z+KPzVZIps957L9/l49I/B5XPgvu/3fNcjKYqiIAiCamgsXYAgCA9GhFYQVEaEVhBURoRWEFRGhFYQVEaEVhBURoRWEFRGhFYQVEaEVhBURoRWEFRGhFYQVEaEVhBURoRWEFRGhFYQVEaEVhBURoRWEFRGhFYQVEaEVhBURoRWEFRGhFYQVEaEVhBURoS2ASjGKirLS6k0ioMthcYnQtsAblw4weeb0zj63U1LlyI0AyK09VbBmfwc1iRnszf3LGZLlyPYPBHaerp59TLHj1ykQl/C/+zZR35ppaVLEmycCG09KKYbnDr5Bd93/D3zXhiCfOEgu49cwWjpwgSbJkJbZwpV5Ze5fLyEviOeZMTw39PP+SKf//NLzlZYujbBlonQ1pVym2sXDvLZ9wbsyyq4SSsefqgNp7Z/wj/ziqi2dH2CzdJZugC1Mt38jkOfHOTf+cWkXzuOQa9QccWE5j9H+N/PjzG2rwcdWlq6SsEWidDWSRVXjx/mnOLDzJdH4vuII1pFgpuX+fCdpSTt38XRpwfSwbe1pQsVbJC4PX5glRQX7mHLur9y4PxxyrX2uLfzwMOjLS00Rgy6Sm7nZ7FxQyr7v72JWG4hNDTR0taByWiPh+8zDDa3wGCuwGhWsNOZqaqswO6xsYR1kLFv5YzZbEQBJEsXLNgUSTxUWhDURdweC4LKiNDWk9ls5saNGxiNYkmF0DREn7aeLl26xObNm+nYsSNPP/00bdq0sXRJgo0Toa2H6upqsrOzefvttzEYDJw8eZLw8HB69uyJJInhJ6FxiIGoOlIUha+++oro6GgOHTqEJEk4Ojri4+NDREQE48aNw9XV1dJlCjZIhLaOvvnmG1auXElGRgbV1dWMGTOG3r17s23bNmRZZuLEiUydOpU+ffqg04kbGqHhiIGoOlAUhezsbD755BO6d++Ovb097u7uxMTEsG7dOjw9PUlMTGTGjBn8/e9/59atW5YuWbAhIrR1kJuby9atW3F0dGTcuHG0atUKrVaLo6MjY8aMISMjgz/+8Y+Ul5ezcOFCYmJiyM3NpbpabCMQ6k+E9gH98MMPbNq0iUuXLjF9+nR69eqFLMsYjUZqehqdO3dmwYIFvPvuu/Ts2ZOsrCyWLFnC9u3buXr1qoWvQFA7EdoHYDQaycrK4m9/+xujRo0iODgYDw8PtFotWq32FyPGrq6ujB8/nuTkZKKiorh8+TKLFy/m9ddf5/Dhw2JeV6gzMULyAM6cOUNaWhoeHh48//zzPPzww1y6dAlFUTCbzdxtTM/Ly4uYmBh69erFpk2b2L59O6dOnSIsLIyAgADc3d3F9JDwQERLW0tXr14lLi7uzm2xn58fACUlJZjN9z7OzWAwMGnSJNasWUNMTAylpaW89tpr/PnPf+bYsWPIstwUlyDYCNHS1kJVVRU7duxg+/btBAQEMGnSJOzt7VEUBb1ej1arRa/X37fF9PLyYtasWfTv35+UlBQ+/vhjCgsLmTJlCs888wwPPfSQaHWF+xKhrYXCwkLS09Px8PBg5syZtGvXDgBJknBxcQF+DHZtprwNBgNDhgyhY8eO9OnTh4yMDFasWMHx48eZMmUK/fr1w87OrlGvR1A3cXt8HyUlJaxevZoLFy4wa9YsnnzySTSaH39tiqJQVlZ2p8WtLY1GQ6dOnZgzZw6rV6/G39+fnTt3Eh4eTmJiIhcvXmysyxFsgGhp7+PDDz9k9+7dDBgwgMmTJ/8inIqiYDKZkGW5Tv1SBwcH/P396dq1K1lZWWzevJnly5dz8OBBIiIi8Pf3F62u8CsitPeQm5tLfHw8np6ezJ49Gzc3t1/8f41Gc2dhRV1JkoSnpyczZ87E29ublJQUdu/eTX5+PhEREQQGBuLp6VnfSxFsiAjtb7h8+TJr167l66+/Zs2aNYwcOfKug0Q1LaxGo6nXIJK9vT3Dhw+ne/fuPPnkk6SmpvL2229z4MABoqKi8PPzo2VLcbyjIEL7m/bv309OTg6jR48mICAAe3v7X32NoiiUl5djNBqprq6u1UDU/Xh4eBAREUGfPn1ISkoiJyeHwsJCpk+fTlhYGK1bixMemzsxEHUXx44dIzU1lW7durFs2TI6d+5816+TJAl7e3vs7OwwGAwNNl3j4ODAkCFDWL16Ne+++y4ajYZXX32VKVOmsH//fqqqqhrk5wjqJEL7X4qLi4mPj+fEiRNMnTqVwYMH3/PrnZ2dURSl1lM+D6JNmzaEhoYSFxfHs88+y4kTJ5g/fz5xcXFcvHixwX+eoA7i9vhnZFlm3759fPjhhwwaNIjx48ff8+sVRaGkpARFUdDpdI2yMMJgMDB8+HB69uyJr68vaWlpvPrqq+Tm5jJjxgyGDRv2QNNNgvqJ0P5ElmUOHz7MqlWraNu2LXPmzKFTp073/B5FUVAUBVmWf3PtcUNp164dM2fOxMfHhw0bNrBjxw5OnjxJSEgIgYGBdO3a9c78sWDbRGh/Ul5eTkpKCmfOnGHx4sWMGDHivt+j0WhwdXX91Q6fxqLT6Rg8eDBeXl706dOHzZs3Exsby/79+4mMjGTcuHF3HTATbIsILT8eg/rxxx+zd+9e/P39CQ4OrvWihtu3bwM0WXAB2rdvz4wZMxg4cCCpqalkZWVx9uxZcnNzmTp1Ko8//ni95o4F6yZCC+Tn57Nx40b0ej0xMTF4eXnV6vtkWeb27duYTKYGm/KpLQcHB5544gk6dOiAt7c3GzZsIDk5mYMHDxITE8Pw4cNp2bKl2IBgg5p9J6i8vJzk5GSOHj3KlClT8PX1rfUbXaPR0KJFC3Q6HXZ2dk0eEEmS7rS68fHxTJgwgdOnTzN79mzeeOMNjh8/3qT1CE2jWYfWZDKRnZ19ZxHF5MmTH7hP6ODggCRJjT4QdS86nY7+/fuzcuVKYmNj6dSpEwkJCcyfP5+srCxKSkosUpfQOJp1aAsKCli3bh2Ojo7MmDGDrl27PtD3y7JMaWkpZrMZSZIseita0+qGh4cTGxtLYGAg586dY9GiRaxYsYKCggKL1SY0rGbbpy0uLmbjxo0UFBTw4osvMmjQoDq9zs+nWaxhsYNWq8XPzw8vLy/8/f1JT08nLS2NkydPMm3aNEaNGoW7u7ulyxTqoVm2tNXV1ezdu5esrCz8/PwYN24cLVq0eODXqZny0Wg09z1ypql5eHgQHBzMmjVriIyM5OTJk7z00ku88cYbXLx40erqFWqvWYa2oKCAd955BwcHB+bMmcNjjz1Wp9dRFIXr168DP+7SsbaRWr1eT69evXjllVeIi4vjkUceITU1lcDAQLZu3Sr6uirV7EJbWlpKamoqRUVFTJ06lSFDhtR5TlNRFKqrqzGbzY2y9rih1Byqvn79embOnElRURExMTEsXbqUL7/8UhznqjLNLrTZ2dlkZ2fj6+tLVFQUjo6OdX4tjUaDk5MTOp2u0dYeNxSdTke3bt14+eWXeeedd+jVqxeZmZksWLCAtLQ0ioqKrPZDR/ilZhXagoICEhIS0Ol0REVF0bZt23q/5s9baTW86Vu1asXkyZNZt24ds2fP5tKlSyxYsIClS5dy4MABVVxDc9dsQnv9+nWSk5M5deoUoaGhDB06tN6vWTPlU3NOlJo88sgjLFu2jPj4eAYOHEhmZiaLFi0iOTlZPLrEyjWL0CqKQlZWFunp6QwdOpTg4OA7R5/WhyRJ6PV6NBpNk649biguLi5MmDCB+Ph4XnzxRYqLi3n55ZdZsmQJBw4cEJvtrVSzCG1eXh4bN27E3t6eyMhIunfv3iCvK0kSrq6uSJLU5GuPG1KPHj2IiYlh7dq1dO/enezsbBYuXEhaWhrfffedpcsT/ovNh7akpIQNGzaQl5fHCy+8wKhRoxqsRVQUhdLSUuD/lzOqVatWrRg7diypqalERkZSXFzM8uXLeemllzh8+LB4TKcVsenQyrJMTk4O27ZtY9SoUYSHhzfoiYY15x6bzWZVt7Q/17VrV1599VVSUlIICAhg9+7dREVFiUPUrYhNL2MsKCggPj4eV1dXnn/+ebp06dKgr6/RaHBxcVFlf/ZeWrRowfDhw+nUqRN9+/Zly5YtvPnmm+Tl5TFt2jSeeOIJsdnegmw2tGVlZWzatInz588zZ84cRo4c2Sg/R1EUJEmyuaNeJEnCy8uLBQsW0L9/f9atW8fOnTv5+uuvCQkJYfLkyXh4eNjUh5Va2GRoTSYT+/btY+fOnfj5+REaGlqvRRS/pebcYzVO+dSWXq9nxIgReHl54evry8aNG4mNjeXkyZOEhYUxYMCAOq3bFurOtpqHn5w8eZKkpCRkWWbevHkNfltco+bcY61Wa/UrouqrU6dOzJ07l4SEBIYOHUp2djbz5s0jMTGR77//3ib682phc6GtqKggMzOTM2fOMHXqVPz8/Br1vCRnZ2cAmxmIuhcHBwf8/PxISEhg+fLl6PV6YmNjWbx4Mfv27ePWrVuWLrFZsKnbY6PRSHZ2Nh988AF9+/ZlypQpjfr8m5opn5pHXdpyS1tDo9Hg7u7OzJkz6dOnDwkJCezdu5f8/HwiIyP5wx/+gKenp8318a2JTf1mCwsLSU5ORqvVEhERcd9zi+tLUZQ7x8zU/NdcODg4MHLkSOLj41m+fDmKotxZTbV3715MJpOlS7RZNtPSlpWVkZmZSUFBAdHR0YwcObLRP+01Gg1ubm5otdpmu6m8bdu2REZG0rt3bzZv3sxHH31EYWEhERERTJw4kYcfftjSJdocmwhtdXU1u3fvJjMzk8GDBxMYGNgoo8V3U1lZCWDzA1H3Ym9vz7Bhw+jRoweDBw9m06ZN/OUvf+GLL74gMjKSIUOGYDAYLF2mzbCJ0J49e5a0tDQcHR0JCwv7zafcNTRZlqmoqMBkMmE0GpvV7fHdtGvXjpCQELy9vUlKSuLTTz/lwoULhIaGMnHiRDp06GDpEm2C6vu0JSUlpKamcvToUYKDgwkICGiyQRCNRoPBYECn06l+7XFDsbOzw8fHh7fffpu33noLvV7Pyy+/THR0NP/4xz/ECHMDUHVoFUVh165d7Nixg/79+xMUFNTky+ucnJxQFIXKyspm39L+nIuLC8HBwSQmJhIWFsZXX31FaGgob731FufOnbN0eaqm6tAWFhayceNGXFxcavWUu4YmyzI//PADsiyLZ+fchSRJ9O7dm9dee43Y2Fh69OhBYmIi8+fPZ/v27XcOxRMejGr7tMXFxaSkpHDixAmio6MZMWKERecGxa3x3UmSRNu2bQkNDaVnz55kZGSwZcsW8vPz72xAeNBD4ps7VYZWURT27t3Ljh078Pb2ZsKECRYZnRRTPrUnSRK+vr531jAnJCSQlJTEkSNHmDFjBmPGjGmyEX+1U2Vojx49SlJSEvb29kRHR/Poo49arJaKioo7t8eitb0/Nzc3goKC6NmzJ1u2bCErK4slS5Zw5MgRQkJC6N69OzqdKt+WTUZ1v53i4mK2bNnCsWPHmD17Nn5+fha7LZZlmcrKSmRZxmQyiYGoWtLpdPTr1w8vLy98fHxISUlh/fr1fPHFF8ybN4/f/e53DXKGl61S3UDU559/TlZWFgMHDiQ0NNSif9yaR11qtdpms/a4Ibm6uvLcc8+xevVqJk+ezLfffktMTAyrVq2ioKBAdDl+g6pCe+LECd577z3s7OyYOXNmnR/n0ZBqppgs+ahLNdPr9Xh7e7NixQpWrlyJl5cXcXFxzJ8/nw8++IDy8nJLl2h1VBPa69evs27dOgoKCggKCmL06NGWLglZlikrKxOBbQAuLi5MmjSJVatWERUVRWFhITExMbzyyiucPn3a0uVZFVX0aauqqsjJyWHr1q307duXqVOnNuqWu9qSJAmtVotGo2nWa48bip2dHX369MHT0xMfHx+Sk5PJyMjgyJEjhIaGEhQUdOfI2uZMFaE9ceIEKSkpODg4MHfu3EY7ieJBSZJEq1atkCRJDEQ1oNatWzNx4kR69OhBRkYGmzdv5vXXX+f48eOEh4fj6+uLnZ2dpcu0GKsP7Y0bN0hPTycvL4/o6Gieeuopq5oSKC8vR1EU0dI2MJ1Oh7e3Nx06dGDAgAEkJiaSmZnJv/71LxYsWMD48eNp3bq1pcu0CKvu05rNZrKysti5cye9e/cmKirKqg4Rk2UZo9FoU+ceWxs3NzcCAwNZv349kZGRlJaWMm/ePBYtWsTBgweb5Qiz9TRZd5GXl0daWhoGg4H58+fz0EMPWbqkX9BoNDg7O6PX60VL28g6d+7M0qVL8fX1JT09nR07dlBQUEBUVBRjx461uvdGY7Lalra0tJStW7dy+PBhQkJCGD16tFWHwpprsxWtW7cmKCiINWvWsHz5ckpLS1m6dClLly7l0KFDzeZOx2pDe+TIETIzMxkyZAhBQUE4OTlZuqRfqTn32Gg0ik3wTUSSJB599FFefPFF1q5dy5NPPklGRgaRkZGsX7+ekpISS5fY6KwytAUFBbz77rs4OTkxd+7cBnvKXUOrOfdYp9NhZ2cnWtsmpNPpCAgI4K9//StvvfUWt27d4k9/+hPz58+3+QeGWV1or169Snp6Orm5uUyYMIGRI0dadRicnZ2RJEm0tBag0Wjo0KEDs2bN4v3332fo0KHs2bOHyMhIkpOTbfYxnVYVWpPJxEcffcS2bdvw8fHhueees4pFFL9FURTKysqQZVmsPbagli1bEhAQQHx8PHPnzqWyspJly5bxyiuv8OWXX1JRUWHpEhuUVYX29OnTpKamotPpWLhwIX379rV0SfdlNpsxm82ipbUwSZJwd3dn8eLFrF27llGjRpGVlUVERAQJCQmcP3/eZqaHrCa01dXVbNu2jdOnT/PUU08xbNgwq2+5alZEiVbWejg4ODB69Gji4uJ46aWX0Ol0rFixgkWLFvHZZ5/dOfJWzaxintZsNvPBBx/cGS2ePn26VY4W343RaAR+XDcrzomyHp6ensybNw8/Pz/i4+PZtWsX58+fZ9KkSYSEhNC5c2fV/r2sIrSFhYWkpqZy8+bNO6fVq0HNLp+qqiquXbvG+fPnsbe3/9VtsiRJtGjRAldXV/R6vYWqbX5atmyJv78/HTt2xMfHh7S0NOLi4jh27BizZs1i8ODBqjzixuKhvXnz5p01pdOmTWPQoEGqeXiTyWTi2rVrmEwm9uzZw9ixY391m1yzEyggIIBFixaJA7stoFOnTkRHRzNo0CASExPZv38/p0+fJjg4mKCgILp27aqqVteioZVlmezsbDZs2EC/fv2YNm0abm5ulizpgSiKQnV1NbIs4+zsTPfu3X/xgSNJEtevX+fYsWN88803Nj13aO0MBgP+/v489thj5OTkkJSUxOrVqzl8+DCRkZGMGDFCNa2uRUN78eJFNmzYgFarZc6cOfTr18+S5dSJJEmYzWaeeOIJNmzYgMFguHN7rNPpyM/PZ+HChar6JLdVNce5hoWF0bt3b9LS0tixYwdnzpwhJCSEyZMn061bN6sfVLRYaG/cuEFSUhKHDx8mPDycp556ylKl1FvN82mdnJx+tc/T0dFRBNbK6HQ6BgwYgJeXF97e3mzZsoW1a9eSl5dHeHg4w4cPt+qD5SzSeTQajezdu5fExER8fHyIioqy6l9SbSiKgizLv/r3u/2bYB3atGnDCy+8wHvvvUdgYCC7du1i4cKFrFq1iitXrli6vN9kkdBeuXKF1atXo9VqiYyMpEePHpYoQxDQarV4e3vz5ptvkpycjIeHB2vXriU8PJyPPvqIGzdu3OO7zdy6+QPffnOBCxcu8J/yW5gVhcrbJhpznU2T3x6Xl5ezceNG8vPzefbZZ61+y11tSZJ01+v4+b/ZwnXaqprjXB9//HESEhL4+OOPWbJkCUFBQYSGhtKlS5dfDDLK1Tf4/sQ/2PnZHvadKKOFXsNDfn708fCg8lZ3ng98FF0j9YqaPLSffvopmzdvpmfPnixcuJA2bdo0dQkNRqvV3tn8Xl1dTXl5+a8GosrLy6msrESSJKqqqqioqLCZ5XQPomYbo8lksnQpv0mSJJydnZkxYwbt27dn3bp1rFmzhqNHjzJ9+nSGDRv2Uzeukn/nZrDmta2Y+gWz4KVn6OImcSk/k/e37aWkSzThUuM99aL+oTVVceX4Hv7n6yvcMmuRkFEUUCQdjh7e+A/vjWdLPRJQVFREeno6Fy5coG/fvhw6dEi1m5drdvYcOHAAo9HIqVOniI2NRa/X37kejUbDlStXOHfuHFVVVSQnJ6PX622yn3u/v6Esy1y6dIlbt25Z/R1HzcChg4MDRUVF5OTkcPToUSIjIwkJDcXD8TYfZnzKiXbj+MvcCHw7/Dj46NF+Fstc25Nx1EyZGdo2UudTUuqbGFMlF/93M+tTt7I99xq9A8bTt509ld9f4J95lfSdPJ0Fz/vjUlXO+2vj+Gt8PMXFxTY1olrzK/ytN2PNPG7Ns2xtiaIoGAwG2rVrV6tnA6v5+p2cXRgzcgiD3av50/t7cA5dScK0J3C0q/m7K9wqv8LFC7dx790FN23jfDjVv6XVOdBxaDDhxdf4uiSPP8xcTNhjLshl35KT8jqvZa+nx6DHeK6bI0OHDsWrc2c0Go2q/3j/TZKke15PzTJGBweHJqyqaSiKgp2dXa2XaFp7K3svChJ2ym2M+Vu4IlXQ3lWD9IvWVKKFiyc9GnlzWoP2aSWNBu1Pny6aVu70eLQNuk8PU1xRjZNTS0aMHNmQP04QLOA23xS7oqBgNklggbangUKrgCRRdb2Es0dyOXTdmeqbl/gk6wc6Pz6ZEd3cEMvkBdugw2Doghdais7+wM0qhZb6/797MFdWcLO4AnuPtjhorPX2+CeSpOHW95f4ImcbP7Sxx2i8TtFtZ4b5t8HVTh0bAATh/vS06TmU0BE5rPpwPdt7eRA+3hsnHSjmMs7t38u/rzjhO3UMDo30tm+w0CqyGZdOPXk6+k9M7uWKXHmZ3K0JvL9+DRel9iwPG4i7xfcUCUL9aV08GTJlAd/8+z0ObVrJf86NoKOrFsV4C4OxFT1HD6ONrvH67g0UIwkJCa3eDie3VrRycgKn7gx6+vf8LekgeQcKuRrUH/fGmm22gOKvd/PZPw9xplhB0rjQ9XE/nh7fn1ZacVdh+7S06TqIOavcOPBpFvvPF3H5loTewZNRE56hb482jbrUsEFCK1feoPzmDW7fvk15SSml10G5fYkvsrZxGjNejz9EW71tvZl1hpbob1zms+0HcBsTRR9nJ3Sod2RUeHD6to8yIuwlRjTxz63/PG3VDU7ueJvYDbv46lIV7by64t5Sj1x9nbLiUnpMWUbkhN/Rt5069irWnkxp7g6WvJZCx8UJLBr+CC1FZoUmUP+WVm+go38YMY9NxKxoUGQZWVEACZ29AfdOXXBvaYNjx4qCLJtR+HF3z0+XLAiNrv6h1ehwav8ovdo3QDWCINyXbXU0BaEZEKEVBJURoa0rSULSaJAkCY1G+ll/1sSFrw9w9Ox/uN38duAJTUAsd6gjc0UpxdeuUX7jJqX/KeLyJTscNWYo/hfrPvyOXr/vRC/bmZYWrIgIbR0VHfobG7Zs4d/Xb1GUsoJzmXZoUJArr2HnF8GkDq2xu//LCMIDq/88bTNlvFlMcdkNqmQtKGZk+cdfo4KGlq5utHZ2RNdIC8aF5k2EVhBURgxECYLKiNAKgsqI0AqCyojQCoLKiNAKgsqI0AqCyojQCoLKiNAKgsqI0AqCyojQCoLKiNAKgsqI0AqCyojQCoLK/B+fvrjvBVq5hgAAAABJRU5ErkJggg==)
Maths-General
Maths-
Simplify √50 - √98 + √162
Simplify √50 - √98 + √162
Maths-General
Maths-
A fish tank is in the shape of a cube . Its volume is 125 Cubic feet . What is the area of one face of the tank ?
A fish tank is in the shape of a cube . Its volume is 125 Cubic feet . What is the area of one face of the tank ?
Maths-General
Maths-
In the adjacent figure, points B, A, D are collinear and AD = AC.
Given that
and
. Find
.
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)
In the adjacent figure, points B, A, D are collinear and AD = AC.
Given that
and
. Find
.
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)
Maths-General
Maths-
In the figure, ABC is a triangle in which
. Show that ![A C squared equals A B squared plus B C squared minus 2 B C times B D](data:image/png;base64,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)
.![](data:image/png;base64,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)
In the figure, ABC is a triangle in which
. Show that ![A C squared equals A B squared plus B C squared minus 2 B C times B D](data:image/png;base64,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)
.![](data:image/png;base64,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)
Maths-General
Maths-
Solve the equation m2 = 14
Solve the equation m2 = 14
Maths-General
Maths-
The traversers are adding a new room to their house. The room will be a cube with a volume of 6589 cubic feet .They are going to put in hardwood floors , which costs Rs 10 per square foot . How much will the hardwood floors cost ?
The traversers are adding a new room to their house. The room will be a cube with a volume of 6589 cubic feet .They are going to put in hardwood floors , which costs Rs 10 per square foot . How much will the hardwood floors cost ?
Maths-General
Maths-
Maths-General
Maths-
The angles of a triangle are
Find the value of and then the angles of the triangle
The angles of a triangle are
Find the value of and then the angles of the triangle
Maths-General
Maths-
D and E are points on the base BC of
such that BD = CE. If AD = AE, prove that
.
![](data:image/png;base64,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)
D and E are points on the base BC of
such that BD = CE. If AD = AE, prove that
.
![](data:image/png;base64,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)
Maths-General
Maths-
Sita has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length of one side of new garage ?
Sita has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length of one side of new garage ?
Maths-General
Maths-
Maths-General
Maths-
In
, DA = DB = DC. Show that
.
![](data:image/png;base64,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)
In
, DA = DB = DC. Show that
.
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)
Maths-General