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

Rationalize the denominator.

`11 / sqrt 3`

Write the lowest rationalising factor of 5√2.

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

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

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 = 2√3 + 2√2 , find : `( x + 1/x)^2`

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)`

Find the value of a and b if `(sqrt(7) - 2)/(sqrt(7) + 2) = asqrt(7) + b`.