Rationalise the denominator of (6 + 5√3 )/√3 Give your answer in its simplest form.

A key component of using Surds is knowing how to multiply them. As such √3 x √3 = 3, √4 x √4 = 4 and so on. The √ sign means the root of this number.

On to the Question given we are asked to rationalise the denominator. This means to remove our root value from the bottom half of the fraction given so that we have a nice whole number instead. Our first step is to realise that by multiplying the bottom by √3 we will instead get 3, but if we only multiply the bottom by √3 then we are changing the value of our fraction overall, so we do the same to the top to keep it the same. After this we have (6√3 + (5√3 x √3))/3, which is equal to (6√3 +15)/3. We are then asked to give our answer in its simplest form, so by cancelling factors we then arrive at our final answer of 2√3 + 5.