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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, $$\frac{ \sqrt{27}} { \sqrt{15}} = \sqrt { \frac{27}{15}}$$

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

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

= $$\normalsize \frac { 3 \sqrt{3}} { \sqrt{5} \sqrt{3}}$$

= $$\normalsize \frac { 3 \sqrt{\not{3}}} { \sqrt{5} \sqrt{\not{3}}}$$

= $$\normalsize \frac { 3} { \sqrt{5}}$$

error: