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

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

Rationalize the denominator.

`5/sqrt 7`

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

`sqrt 27`

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

`4 sqrt 11`

Write the lowest rationalising factor of : √13 + 3

Write the lowest rationalising factor of 15 – 3√2.

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

Find the values of 'a' and 'b' in each of the following:
`( sqrt7 - 2 )/( sqrt7 + 2 ) = asqrt7 + b`

Find the values of 'a' and 'b' in each of the following:
`[5 + 3sqrt2]/[ 5 - 3sqrt2] = a + bsqrt2`

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

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