Topic Content:
- Multiplication & Division of Surds
Example 1.4.1:
Evaluate the following:
(a) \( \scriptsize \sqrt{27} \: \times \: \sqrt{15} \)
(b) \( \frac{ \sqrt{27}} { \sqrt{15}} \)
Solution
(a) \( \scriptsize \sqrt{27} \: \times \: \sqrt{15} \)
\( \left (\scriptsize \sqrt{3 \: \times \: 9} \right) \: \times \: \left (\scriptsize \sqrt{3 \: \times \: 5} \right)\)= \( \scriptsize\sqrt{3} \: \times \: \sqrt{9}\: \times \: \sqrt{3} \: \times \: \sqrt{5}\)
= \( \scriptsize\sqrt{3} \: \times \: \sqrt{3}\: \times \: \sqrt{9} \: \times \: \sqrt{5}\)
= \(\scriptsize 3 \: \times \: \ 3\: \times \: \ \sqrt{5}\)
= \( \scriptsize 9 \sqrt{5}\)
(b) \( \frac{ \sqrt{27}} { \sqrt{15}} \)
from the second rule of surds:
\(\sqrt { \frac{a}{b}} = \frac {\sqrt {a}}{\sqrt {b}} \)
Therfore, \( \frac{ \sqrt{27}} { \sqrt{15}} = \sqrt { \frac{27}{15}} \)
= \( \normalsize \frac{ \left ( \sqrt{3 \: \times \: 9} \right)}{\left (\sqrt{3 \: \times \: 5} \right)}\)
= \(\normalsize \frac{ \sqrt{3} \: \times \: \sqrt{9}}{\sqrt{3} \: \times \: \sqrt{5}}\)
= \( \normalsize \frac { 3 \sqrt{3}} { \sqrt{5} \sqrt{3}} \)
= \( \normalsize \frac { 3 \sqrt{\not{3}}} { \sqrt{5} \sqrt{\not{3}}} \)
= \( \normalsize \frac { 3} { \sqrt{5}} \)
