Maths-
General
Easy
Question
Classify whether the following Surd is rational or irrational , justify 4√5+ 9
Hint:
Use properties of rational and irrational numbers.
The correct answer is: irrational number.
Complete step by step solution:
(It is an irrational number)
(It is a rational number)
Here one number is irrational and the other is rational.
On addition, we have
, we get an irrational number.
(Since rational number + irrational number = irrational number)
This cant be written in the form
, where p and q are integers.
∴
is an irrational number.
Related Questions to study
Maths-
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
Maths-General
Maths-
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify 8-√48
Classify whether the following Surd is rational or irrational , justify 8-√48
Maths-General
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Classify whether the following Surd is rational or irrational , Justify.√47+√8
Classify whether the following Surd is rational or irrational , Justify.√47+√8
Maths-General
Maths-
In the figure, sides QP and RQ of a
are produced to points S and T respectively.
If
and
, find
.
![](data:image/png;base64,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)
In the figure, sides QP and RQ of a
are produced to points S and T respectively.
If
and
, find
.
![](data:image/png;base64,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)
Maths-General
Maths-
Simplify √8 - √18 + √50
Simplify √8 - √18 + √50
Maths-General
Maths-
Maths-General
Maths-
Prove in the given figure, side QR of a
is produced to a point S.
If the bisector of
and
meet at the point T, then prove
![straight angle QTR equals 1 half straight angle QPR](data:image/png;base64,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)
![](data:image/png;base64,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)
Prove in the given figure, side QR of a
is produced to a point S.
If the bisector of
and
meet at the point T, then prove
![straight angle QTR equals 1 half straight angle QPR](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
In an equilateral triangle ABC,D is a point on the side BC , such that
. Prove that
![9 AD squared equals 7 AB squared](data:image/png;base64,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)
In an equilateral triangle ABC,D is a point on the side BC , such that
. Prove that
![9 AD squared equals 7 AB squared](data:image/png;base64,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)
Maths-General
Maths-
In the figure, find the value of x.
![](data:image/png;base64,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)
In the figure, find the value of x.
![](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Simplify √12 - √48 +√1323
Simplify √12 - √48 +√1323
Maths-General
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,iVBORw0KGgoAAAANSUhEUgAAAF8AAAAjCAYAAADyrNZPAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAApdJREFUeNrtmkFkXEEYx0c8FVWhp7WqQkRED71UVfRQpaoqqkJE9NBDyKGnHHqr6KHK6qmqSkRV5VBiRVVUqVpROYSqqh6qRM655BBRK8L2//F/PNOZl3nZ3feSt9+fPzuz3+bxm5lvvpkXY8qvEXge/mFUuWsJnoVbiqI4KXyFr/BVCl/hqxR+d1SDd+maws8X/Dpcpb8WOAA9B3+P0GNVuQLKBv9mu3/gGmdmE/4L1+EhR9wA/AreoBfYd1zhtxzupITFu4C4ubSR+wVfhvvgCJ6Bf8MVK/YLfCfRHmdfSNpZLzjvd1oy8XbgK4fETcH75Pqfvnlm+ST8zGq/cMQ9h6dTBmCPrh2zdNGO3gaCPwv/hD/Dd10BB54fyir4nmjXPfntOr/rlY1yKRB8vDpkYt6HX7oCNuFLjv5B5v9Y8sBTjjjp2+4R+PUM4MfgVX6ukLMzvWxx0+2jxznr9wNWiLHiyghfmKxkAB8xnZ9P9AnPUV+102C1I16Gh62Znwa/2cXqJLRaaR3RISCzgBc9hh9afU/hB6Eg+llOxtr2pJ3+EqediKkjC/hRa69MTvAPoQ+WjfSJle9ueUrVMm64MtE+ZgRveF7yrTJvyWkcy+Rcoj0BLzri3qSUmicVvqzmT0cAP8vS2yc5kN22D04TiZQiwOetw1SsBk9rEeMfwWslu5M5TSZZwVdZ059JiZmxB+cGoR7w+C+jczHl0PA6cQ2xcMjDTqIaGTfs+HphmVVimmRi/zEl11XuQ7vMs/KvI/eMKhetcR+KV+UF3i1NK5piNMicrCpITUVQjMaYelQF1O0b3IhVOUrK4/emA6/7VNk0RPDDiiJfyQXXIk+sqhxV4YkzUhT5a9V4Xlyouq92Xp7kon+pXsa6oKW7/QAAAMV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bW4+OTA8L21uPjxtbz4mI3gyMjE4OzwvbW8+PC9tc3VwPjxtbz4rPC9tbz48bWZyYWM+PG1uPjE8L21uPjxtbj4yPC9tbj48L21mcmFjPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj4mI3gyMjIwOzwvbWk+PG1pPkE8L21pPjwvbWF0aD7BFYtfAAAAAElFTkSuQmCC)
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,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)
Maths-General