Simplify fully: (24 - √ 300)/(4√ 3 - 5). Give your answer in the form a√ b where a and b are integers and find the values of a and b.

rationalise the denominator (remove the surds) by multiplying by a fraction = 1, known as the rationalising factor = (24 - √ 300)/(4√ 3 - 5) * (4√ 3 + 5)/(4√ 3 + 5) = (24 - √ 300)(4√ 3 + 5)/(48 - 25) = (24 - √ 300)(4√ 3 + 5)/23 expand the brackets of the numerator and group like terms = (24 - 10√ 3)(4√ 3 + 5)/23 = (24 * 4√ 3 - 4√ 3 * 10√ 3 + 24 * 5 - 5 * 10√ 3)/23 = (96√ 3 - 120 + 120 - 50√ 3)/23 eliminate like terms = ((96 - 50)√ 3 + (120 - 120))/23 = (46√ 3 + 0)/23 = (46√ 3)/23 divide by common factor = 2√ 3 a = 2 b = 3