# How do you simplify sqrt (18) / (sqrt (8) - sqrt (2))?

May 16, 2018

Simplify each radical individually, and then work with the fraction as a whole. You will find that the simplified version is $3$

#### Explanation:

First, we'll simplify the numerator:

$\sqrt{18} = \sqrt{9 \times 2}$

$\sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}$

sqrt(9)xxsqrt(2)=3xxsqrt(2)=color(orange)(3sqrt(2)

Now the expression can be written as:

$\frac{\textcolor{\mathmr{and} a n \ge}{3 \sqrt{2}}}{\sqrt{8} - \sqrt{2}}$

Next, we'll simplify the denominator:

$\sqrt{8} - \sqrt{2} = \sqrt{4 \times 2} - \sqrt{2}$

$\sqrt{4 \times 2} - \sqrt{2} = \sqrt{4} \times \sqrt{2} - \sqrt{2}$

$\sqrt{4} \times \sqrt{2} - \sqrt{2} = 2 \times \sqrt{2} - \sqrt{2} = 2 \sqrt{2} - \sqrt{2}$

$2 \sqrt{2} - \sqrt{2} = \left(2 - 1\right) \sqrt{2} = \textcolor{b l u e}{\sqrt{2}}$

Re-write the expression again:

$\frac{\textcolor{\mathmr{and} a n \ge}{3 \sqrt{2}}}{\textcolor{b l u e}{\sqrt{2}}}$

Finally, we can simplify the fraction:

$\frac{3 \cancel{\sqrt{2}}}{\cancel{\sqrt{2}}} = \textcolor{g r e e n}{3}$