# How do you simplify sqrt18 div sqrt(8 - 3)?

Apr 7, 2015

$\frac{\sqrt{18}}{\sqrt{8 - 3}}$

$= \frac{\sqrt{18}}{\sqrt{5}}$

$= \frac{\sqrt{9 \cdot 2}}{\sqrt{5}}$

$= \frac{\sqrt{9} \cdot \sqrt{2}}{\sqrt{5}}$ We used the Identity $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

$= \frac{3 \cdot \sqrt{2}}{\sqrt{5}}$ -------------(a)

Next, we need to RATIONALISE the denominator.
To do that, we multiply the Numerator and the Denominator by $\sqrt{5}$

$= \frac{3 \cdot \sqrt{2}}{\sqrt{5}}$$\cdot$$\frac{\sqrt{5}}{\sqrt{5}}$

$= \frac{3 \cdot \sqrt{10}}{5}$

The answer can be left in this form, but if you want to find the numerical value of the expression, we can substitute the approximate values of $\sqrt{2}$ and $\sqrt{5}$ in (a)

We get ((3) * (1.414))/2.236 ~ 1.9

Apr 7, 2015

The answer is $3 \sqrt{\frac{2}{5}}$ or $\frac{3 \sqrt{10}}{5}$.

$\sqrt{18}$$\div$$\sqrt{8 - 3}$ =

$\frac{\sqrt{18}}{\sqrt{8 - 3}}$ =

$\frac{\sqrt{2} \sqrt{9}}{\sqrt{5}}$ =

($\sqrt{9} = 3$)

$\frac{3 \sqrt{2}}{\sqrt{5}}$ =

$3 \sqrt{\frac{2}{5}}$

To remove $\sqrt{5}$ from the denominator, multiply the numerator and denominator by $\sqrt{5}$.

$\frac{3 \sqrt{2}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$ =

$\frac{3 \sqrt{2} \cdot \sqrt{5}}{5}$ =

$\frac{3 \sqrt{10}}{5}$