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.

`6/(9sqrt 3)`

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

`3/5 sqrt 10`

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

Find the values of 'a' and 'b' in each of the following:
`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`

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

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

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

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

Rationalise the denominator and simplify `(sqrt(48) + sqrt(32))/(sqrt(27) - sqrt(18))`

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