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.

`3 /sqrt5`

Rationalize the denominator.

`6/(9sqrt 3)`

Write the lowest rationalising factor of √5 - 3.

Write the lowest rationalising factor of : √13 + 3

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : y²

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find m²

If √2 = 1.4 and √3 = 1.7, find the value of : `1/(3 + 2√2)`

Rationalise the denominator `sqrt(75)/sqrt(18)`

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).