If x = 23+22, find: 1x - Mathematics

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

Sum

`1/x = 1/[2sqrt3 + 2sqrt2] xx [2sqrt3 - 2sqrt2]/[2sqrt3 - 2sqrt2]`

= `[2sqrt3 - 2sqrt2]/[(2sqrt3)^2 - (2sqrt2)^2]`

= `[2sqrt3 - 2sqrt2]/(12 - 8)`

= `[cancel(2)^1(sqrt3 - sqrt2)]/cancel(4)_2`

= `(sqrt3 - sqrt2)/2`

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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 8.1 | Page 22

Rationalize the denominator.

`6/(9sqrt 3)`

Write the lowest rationalising factor of 5√2.

Write the lowest rationalising factor of : √18 - √50

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

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

x² + y² + xy.

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

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.

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

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