If M = 1/ 3 - 2sqrt2 and N = 1/3 + 2sqrt2 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 7.2 | Page 22

Rationalize the denominator.

`11 / sqrt 3`

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 : 7 - √7

Find the values of 'a' and 'b' in each of the following :
`[2 + sqrt3]/[ 2 - sqrt3 ] = a + bsqrt3`

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

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

Rationalise the denominator `(3sqrt(5))/sqrt(6)`

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

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