# How do you simplify 2 sqrt11 + sqrt44?

Jun 5, 2016

Writing $44$ as product of its factors.

#### Explanation:

To simplify this you have to search for something you cah do in the square root. You can notice that $44 = 11 \cdot 4$ then we have

$\sqrt{44} = \sqrt{11 \cdot 4}$

and we know that we can separate the square root of a product in the product of the square roots (be careful with this rule, it is valid only for multiplications and divisions, not for sum and subtraction).

$\sqrt{44} = \sqrt{11 \cdot 4} = \sqrt{11} \sqrt{4} = 2 \sqrt{11}$

Then we have the initial expression:

$2 \sqrt{11} + \sqrt{44}$

and now I substitute what I obtained for $\sqrt{44}$

$2 \sqrt{11} + \sqrt{44} = 2 \sqrt{11} + 2 \sqrt{11} = 2 \left(2 \sqrt{11}\right) = 4 \sqrt{11}$.