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

AL
Answered by Aloysius L. Maths tutor

6064 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

If an equation of a line is y=2x+4 and it crosses the x axis at point R, what is the value of x?


How should I calculate the values of a and b when a(4x+12) is equivalent to 2x+36b?


Solve x2 + 2x − 4 = 0 leave in simplest form.


I find the percentage questions really hard, how do I answer the questions that will come up in exams?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning