# How do you simplify (6-sqrt20) / 2?

Feb 24, 2016

$3 - \sqrt{5}$

#### Explanation:

First, recognize that we can simplify $\sqrt{20}$, since $20 = 4 \times 5$.

We can split up a square root through the rule that

$\sqrt{a \times b} = \sqrt{a} \sqrt{b}$

So,

$\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \sqrt{5} = 2 \sqrt{5}$

Thus, the expression equals

$\frac{6 - 2 \sqrt{5}}{2}$

We can split up the fraction:

$\frac{6}{2} - \frac{2 \sqrt{5}}{2}$

Which equals

$3 - \sqrt{5}$

Feb 26, 2016

A very slight variation in presentation. Also written with a lot of detail about each step.

$\text{ } 3 - \sqrt{5}$

#### Explanation:

Looking for common factors. 6 and 20 are even so have a factor of 2. As the denominator is 2 as well we have a first step in simplification

Write as: $\text{ } \frac{6}{2} - \frac{\sqrt{20}}{2}$

$\text{ } \frac{2 \times 3}{2} - \frac{\sqrt{2 \times 10}}{2}$

But $2 \times 5 = 10$ so we now have

$\text{ } \left(\frac{2 \times 3}{2}\right) - \left(\frac{\sqrt{{2}^{2} \times 5}}{2}\right)$

$\text{ } \left(\frac{2}{2} \times 3\right) - \left(\frac{2 \sqrt{5}}{2}\right)$

$\text{ } \left(1 \times 3\right) - \left(\frac{2}{2} \times \sqrt{5}\right)$

$\text{ } \left(1 \times 3\right) - \left(1 \times \sqrt{5}\right)$

$\text{ } 3 - \sqrt{5}$