How do I simplify a fraction with surds on the bottom when the surd is part of a function?
When doing questions like this you simply times the top and bottom of the fraction by the bottom function but with a sign change. For example if "5 - √3" was the denominator of the fraction (on the bottom of the fraction) you would times the top and bottom of the fraction by "5 + √3". Note that it is only the sign in front of the surd that changes.
Here is a worked example of an exam question:
(4 + 2√2) / (2 - √2)
(4 + 2√2)(2 + √2) / (2 - √2)(2 + √2)
Use FOIL to expand the brackets: (8 + 4√2 + 4√2 + 4) / (4 + 2√2 - 2√2 -2)
SIMPLIFY
(12 + 8√2) / 2 = 6 + 4√2
CW
Related Maths GCSE answers
All answers ▸what is: a) 1/3 +1/4 ? b) 4/6 + 3/12?
f(x) = (2x+3)/(x-4). Work out f^-1 (x)
We are given a right angled triangle with one side of unknown length. The shortest side is 3cm long, and the longest side is 5cm long. Calculate the remaining side.
Prove that the square of an odd number is always 1 more than a multiple of 4