Surds - Rationalising the Denominator (AQA A-Level Mathematics): Flashcards

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Surds - Rationalising the Denominator
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Why are surds in denominators bad?

They are not in acceptable/simplified form

Term for rationalized denominator result

Simplified surd form

What to multiply by to rationalize ab\frac{a}{\sqrt{b}}?

bb\frac{\sqrt{b}}{\sqrt{b}}

Conjugate of a+bca + b\sqrt{c}

abca - b\sqrt{c}

What to multiply by when denominator is a+bca + b\sqrt{c}?

abcabc\frac{a - b\sqrt{c}}{a - b\sqrt{c}}

(a+b)(ab)(a + \sqrt{b})(a - \sqrt{b}) simplifies to

a2ba^2 - b

First step when simplifying surd expressions?

Simplify any surds first

Are negative denominators acceptable?

No, they are bad in the examiner's eyes

(3+2)(32)(3 + \sqrt{2})(3 - \sqrt{2}) equals

77

Concept used with conjugates to rationalize

Difference of two squares

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