Rationalising denominatorsIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

What does it mean to rationalise a denominator?
\frac{a}{\sqrt b}=?
\frac{6}{\sqrt3}
\frac{4}{\sqrt8}
What is the conjugate of 3+\sqrt2?
(b+\sqrt c)(b-\sqrt c)=?
\frac{1}{3+\sqrt2}
\frac{2}{4-\sqrt3}
\sqrt{18} in simplest form
\sqrt{12}\times\sqrt6
\sqrt{18}+\sqrt8
\frac{1}{\sqrt{n+1}+\sqrt n}=?
(2+\sqrt3)(2-\sqrt3)

Exam questions on Rationalising denominators

Lena is rationalising the denominators of fractions without a calculator.
Rationalise the denominator of $\frac{4}{\sqrt8}$ and simplify your answer.2 marks
Tomas is simplifying expressions that contain surds, without a calculator.
Simplify $\sqrt{12}\times\sqrt6$ , giving your answer in the form $a\sqrt b$ where $b$ is as small as possible.2 marks
A rectangular banner has area $12$ m $^2$ . Give all answers as exact values with rational denominators.
The length of the banner is $\sqrt6$ m. Find its width.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).