If m = and13-22andn=13+22, find mn - Mathematics

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

Sum

mn = ( 3 + 2√2 )( 3 - 2√2 )

= (3)² - (2√2)²

= 9 - 8

= 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 7.3 | Page 22

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

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

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

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

If x = 2√3 + 2√2, find: `(x + 1/x)`

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

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

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

Rationalise the denominator and simplify `(5sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2))`

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