# How do you solve sqrt(50)+sqrt(2) ?

Sep 9, 2015

You can simplify $\sqrt{50} + \sqrt{2} = 6 \sqrt{2}$

#### Explanation:

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$ and $\sqrt{{a}^{2}} = a$

So:

$\sqrt{50} + \sqrt{2} = \sqrt{{5}^{2} \cdot 2} + \sqrt{2} = \sqrt{{5}^{2}} \sqrt{2} + \sqrt{2}$

$= 5 \sqrt{2} + 1 \sqrt{2} = \left(5 + 1\right) \sqrt{2} = 6 \sqrt{2}$

In general you can try to simplify $\sqrt{n}$ by factorising $n$ to identify square factors. Then you can move the square roots of those square factors out from under the square root.

e.g. $\sqrt{300} = \sqrt{{10}^{2} \cdot 3} = 10 \sqrt{3}$