Question

Find the value of a and b in the following:

`(4sqrt(3))/(2 - sqrt(3)) = a + bsqrt(3)`

Answer 1

We are given:

`(4sqrt(3))/(2 - sqrt(3)) = a + bsqrt(3)`

Step 1: Multiply numerator and denominator by the conjugate of the denominator:

`(4sqrt(3))/(2 - sqrt(3)) xx (2 + sqrt(3))/(2 + sqrt(3))`

= `(4sqrt(3)(2 + sqrt(3)))/((2 - sqrt(3))(2 + sqrt(3))`

Step 2: Simplify the denominator:

`(2 - sqrt(3))(2 + sqrt(3))`

= 4 – 3

= 1

So we just need to expand the numerator:

`4sqrt(3)(2 + sqrt(3))`

= `8sqrt(3) + 4 xx 3`

= `8sqrt(3) + 12`

Step 3: Rearrange:

`8sqrt(3) + 12 = 12 + 8sqrt(3)`

a = 12, b = 8