Exercise 1a (Discussion)

For $\sqrt{mn}$

$\sqrt{mn} = \sqrt{m \times n}$

Substitute the given values;

$ = \sqrt{9 \times 4}$

$ = \sqrt{36}$

$ = 6$

For $\sqrt{m} \times \sqrt{n}$

Substitute the given values

$ = \sqrt{9} \times \sqrt{4}$

$ = 3 \times 2$

$ = 6 $

$ \therefore \sqrt{mn}  =  \sqrt{m} \times \sqrt{n}$

Given that $m=9$ and $n=4$

For $\sqrt{m+n}$:

Substitute the values into the expression

$\sqrt{m+n}$

$=\sqrt{9+4}$

$=\sqrt{13}$

For $\sqrt{m} + \sqrt{n}$:

Substituting the values

$\sqrt{m} + \sqrt{n}$

$=\sqrt{9} + \sqrt{4}$

$=3+2$

$=5$

$\therefore \sqrt{m+n} \neq \sqrt{m} + \sqrt{n}$

Given that $m=9$ and $n=4$;

For $\sqrt{\frac{m}{n}}$;

$\sqrt{\frac{m}{n}}$

$=\sqrt{\frac{9}{4}}$

$=\frac{3}{2}$

For $\frac{\sqrt{m}}{\sqrt{n}}$;

$=\frac{\sqrt{9}}{\sqrt{4}}$

$=\frac{3}{2}$

$\therefore \sqrt{\frac{m}{n}} = \frac{\sqrt{m}}{\sqrt{n}}$