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Mathematical Methods · Unit 1 · Surds and quadratic functions · Surds

Simplify square roots of natural numbers which contain perfect square factors, e.g. √45 = √9 × 5 = √9√5 = 3√5

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Question 1

Simplify $\sqrt{108}$

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Question 2

Simplify \(\sqrt{1{,}152}\) by expressing it in the form \(a\sqrt{b}\), where \(a\) and \(b\) are positive integers and \(b\) has no perfect square factors greater than 1.

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Question 3

Simplify \(\sqrt{108}\).

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Question 4

Simplify √252, expressing your answer in the form a√b where a and b are positive integers and b contains no perfect square factors greater than 1.

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Question 5

Simplify the following expressions, showing all steps. Express each answer in the form \( a\sqrt{b} \) where \( a \) and \( b \) are positive integers and \( b \) contains no perfect square factors. (a) \( \sqrt{1{,}125} \) [2 marks] (b) \( \frac{\sqrt{2{,}352}}{\sqrt{8}} \) [2 marks]

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More in Surds

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Rationalise the denominator of fractional expressions involving square roots, e.g. √7 √3 = √7 √3 × √3 √3 = √7×√3 √3×√3 = √21 3
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Understand the concept of a surd as an irrational number represented using a square root or a radical sign.
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