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

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

Write the lowest rationalising factor of : 7 - √7

Write the lowest rationalising factor of : √5 - √2

Find the values of 'a' and 'b' in each of the following :
`[2 + sqrt3]/[ 2 - sqrt3 ] = a + bsqrt3`

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :
x²

If x = 2√3 + 2√2, find: `(x + 1/x)`

If x = 2√3 + 2√2 , find : `( x + 1/x)^2`

If x = 1 - √2, find the value of `( x - 1/x )^3`

If x = 5 - 2√6, find `x^2 + 1/x^2`

Rationalise the denominator `(3sqrt(5))/sqrt(6)`

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