Question

How do you simplify `2 sqrt11 + sqrt44`?

Answer 1

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*4` then we have

`sqrt(44)=sqrt(11*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*4)=sqrt(11)sqrt(4)=2sqrt(11)`

Then we have the initial expression:

`2sqrt(11)+sqrt(44)`

and now I substitute what I obtained for `sqrt(44)`

`2sqrt(11)+sqrt(44)=2sqrt(11)+2sqrt(11)=2(2sqrt(11))=4sqrt(11)`.