If X =Sqrt5 - 2/Sqrt5 + 2 and Y = Sqrt5 + 2/ Sqrt5 - 2 Find : Xy

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : xy

Sum

xy = `[(sqrt5 - 2)(sqrt5 + 2)]/[(sqrt5 + 2)(sqrt5 - 2)] = 1`

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Rationalisation of Surds

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Chapter 1: Rational and Irrational Numbers - Exercise 1 (C) [Page 22]

Chapter 1 Rational and Irrational Numbers
Exercise 1 (C) | Q 6.3 | Page 22

Rationalize the denominator.

`1/sqrt14`

Rationalize the denominator.

`5/sqrt 7`

Write the simplest form of rationalising factor for the given surd.

`3 sqrt 72`

Write the lowest rationalising factor of 5√2.

Write the lowest rationalising factor of : √13 + 3

If x = 5 - 2√6, find `x^2 + 1/x^2`

If `[ 2 + sqrt5 ]/[ 2 - sqrt5] = x and [2 - sqrt5 ]/[ 2 + sqrt5] = y`; find the value of x² - y².

Find the value of a and b if `(sqrt(7) - 2)/(sqrt(7) + 2) = asqrt(7) + b`.

If x = `sqrt(5) + 2`, then find the value of `x^2 + 1/x^2`

Given `sqrt(2)` = 1.414, find the value of `(8 - 5sqrt(2))/(3 - 2sqrt(2))` (to 3 places of decimals).