Rationalise the denominator and simplify 53+23+2

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

Sum

`(5sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2)) = ((5sqrt(3) + sqrt(2))(sqrt(3) - sqrt(2)))/((sqrt(3) + sqrt(2))(sqrt(3) - sqrt(2))`

= `(5(3) - 5sqrt(3) xx sqrt(2) + (sqrt(2)sqrt(3) - (2)))/((sqrt(3))^2 - (sqrt(2))^2`

= `(15 - 5sqrt(6) + sqrt(6) - 2)/(3 - 2)`

= `(13 - 4sqrt(6))/1`

= `13 - 4sqrt(6)`

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Rationalisation of Surds

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Chapter 2: Real Numbers - Exercise 2.7 [Page 70]

Chapter 2 Real Numbers
Exercise 2.7 | Q 2. (ii) | Page 70

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

`sqrt 32`

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :
x²

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

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

If x = 5 - 2√6, find `x^2 + 1/x^2`

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

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

Rationalise the denominator and simplify `(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6))`

If x = `sqrt(5) + 2`, then find the value of `x^2 + 1/x^2`

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