Laws of Indices & Surds (Edexcel A-Level Mathematics): Flashcards

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Manipulating Surds
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Definition of a surd

Irrational root of a rational number

Type of number a surd is

Irrational

p\sqrt{p} where pp is prime

A surd

35+253\sqrt{5} + 2\sqrt{5}

555\sqrt{5}

Can 52335\sqrt{2} - 3\sqrt{3} simplify?

No, different radicands

2×3\sqrt{2} \times \sqrt{3}

6\sqrt{6}

2×32 \times \sqrt{3}

232\sqrt{3}

45\sqrt{45} in simplified form

353\sqrt{5}

Is 42\sqrt{42} simplified?

Yes

25625^6 as power of 55

5125^{12}

3232 as power of 44

4524^{\frac{5}{2}}

Method for solving index equations

Same base both sides, equate powers

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