Question

Find the value of a and b in the following:

`1/(4 + sqrt(15)) = a + bsqrt(15)`

Answer 1

We are given:

`1/(4 + sqrt(15)) = a + bsqrt(15)`

Step 1: Rationalise the denominator

Multiply numerator and denominator by the conjugate of the denominator `(4 - sqrt(15))`:

`1/(4 + sqrt(15)) = (1 xx (4 - sqrt(15)))/((4 + sqrt(15))(4 - sqrt(15))`

Step 2: Simplify

Denominator: `(4 + sqrt(15))(4 - sqrt(15))`

= 16 – 15

= 1

Numerator: `4 - sqrt(15)`

So, `1/(4 + sqrt(15)) = 4 - sqrt(15)`

a = 4, b = –1