Lesson 1, Topic 4
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Multiplication & Division of Surds

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Evaluate the following:

(a) \( \scriptsize \sqrt{27} \: \times \: \sqrt{15} \)

(b) \( \frac{ \sqrt{27}} { \sqrt{15}} \)

Solution

(a) \( \scriptsize \sqrt{27} \: \times \: \sqrt{15} \)

\( \left (\scriptsize \sqrt{3 \: \times \: 9} \right) \: \times \: \left (\scriptsize \sqrt{3 \: \times \: 5} \right)\)

= \( \scriptsize\sqrt{3} \: \times \: \sqrt{9} \: + \: \sqrt{3} \: \times \: \sqrt{5}\)

= \(\scriptsize 3 \: \times \: \ 3\: \times \: \ \sqrt{5}\)

= \( \scriptsize 9 \sqrt{5}\)

(b) \( \frac{ \sqrt{27}} { \sqrt{15}} \)

from the second rule of surds

\(\sqrt { \frac{a}{b}} = \frac {\sqrt {a}}{\sqrt {b}} \)

Therfore, \( \frac{ \sqrt{27}} { \sqrt{15}} = \sqrt { \frac{27}{15}} \)

= \( \normalsize \frac{ \left ( \sqrt{3 \: \times \: 9} \right)}{\left (\sqrt{3 \: \times \: 5} \right)}\)

= \(\normalsize \frac{ \sqrt{3} \: \times \: \sqrt{9}}{\sqrt{3} \: \times \: \sqrt{5}}\)

= \( \normalsize \frac { 3 \sqrt{3}} { \sqrt{5} \sqrt{3}} \)

= \( \normalsize \frac { 3 \sqrt{\not{3}}} { \sqrt{5} \sqrt{\not{3}}} \)

= \( \normalsize \frac { 3} { \sqrt{5}} \)

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