How do I rationalised and simplify surds?

Say I have a fraction with 2 surds, such as √10 / √6. To rationalise this, we need to get the dominator (bottom fraction) to be an integer. As √10 / √6 x 1 still gives √10 / √6, and we can write 1 as √6 / √6, we can do (√10 / √6) x (√6 / √6) = √(10 x 6) / 6 = √60 / 6.

This is now rationalised, as the demonator is no longer a surd, however it is not in its simplest form yet. To get this we can simplify √60 to give √(4 x 15) = √4 x √15 = 2√15. In the fraction this gives 2√15 / 6 which cancels down to √15 / 3.

TG
Answered by Tabitha G. Maths tutor

4150 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

A and B are on the line 3x+2y=6. At A x=0, what is y? At B y=0, what is x?


How can you calculate the distance between 2 points in a grid if they're not on the same horizontal or vertical line?


Expand and simplify (x-2)(2x+3)(x+1)


If f(x)=8x-3, what is the inverse function?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences