If X = 2√3 + 2√2 , Find : ( X + 1/X)^2 - Mathematics

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

Sum

`( x + 1/x)^2 = [ 5sqrt3 + 3sqrt2/2]^2`

= `( 75 + 18 + 30sqrt6)/4`

= `( 93 + 30sqrt6)/4`

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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 8.3 | Page 22

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

`sqrt 27`

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

`3 sqrt 72`

Write the lowest rationalising factor of : 7 - √7

Write the lowest rationalising factor of : 3√2 + 2√3

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

If x = `2sqrt3 + 2sqrt2`, find: `1/x`

Show that :
`1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5`

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

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

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