Rationalise the denominator of 6/√3 and simplify your answer.

'Rationalise the denominator' means that we need to express the fraction in a way which does not have a surd on the bottom. A surd is a way of expressing an irrational number. For example √4 = 2 which is a rational number so this is not a surd, however √3 = 1.73205... which is called an irrational number because the the numbers after the decimal point keep going on forever. So instead of writing 1.73205... we leave it in the form √3 which is known as a surd. To rationalise the denominator we must multiply both the top and bottom of the fraction by √3. This will make the numerator 6 x √3 which we can write as 6√3. 6 x √3 = 6√3On the denominator we have √3 x √3. When multiplying surds remember the rule √a x √b = √(a x b) so the denominator becomes √9 = 3. Notice that when multiplying two square roots of a number, you get the number itself.√3 x √3 = √(3 x 3) = √9 = 3Our fraction is now (6√3)/3 which we can simplify to 2√3 by dividing both the numerator and denominator by 3. (6√3)/3 = 2√3The final answer is 2√3