Question

How do you simplify `sqrt13+sqrt52`?

Answer 1

`3sqrt(13)`

Explanation:

Given: `sqrt(13)+sqrt(52)`

We have:

`sqrt(52)`

`=sqrt(13*4)`

Using `sqrt(ab)=sqrt(a)sqrt(b) \ "for" \ a,b>=0`.

`=sqrt(4)*sqrt(13)`

`=2sqrt(13)` (only use principal square root)

So, the expression becomes

`<=>sqrt(13)+2sqrt(13)`

Factoring,

`sqrt(13)(1+2)`

`=3sqrt(13)`

Answer 2

`3sqrt13`

Explanation:

With any surd, we can use the law:

`sqrta xx sqrtb=sqrtab`

Simplifying `sqrt13`

`->` Since it is a prime number it cannot be simplified any further

Simplifying `sqrt52`

We can figure out that we can get `52` from `13 xx4`

`therefore` `-> sqrt13 xxsqrt4`

As said earlier, `sqrt13` cannot be simplified, but `sqrt4` can, using our squared numbers of `1,4,9,12,25...`, `sqrt4=2`

Therefore this turns to:

`2sqrt13` as we always put the value in front of the square root#

Adding the surds:

Since we simplified the surds, we can plug these values back in to get:

`sqrt13+2sqrt13`

Since `sqrt13` means `1sqrt13` we can just add both `1` and `2` to get us `3sqrt13` as the root of `sqrt13` is the same in both expressions.

`therefore` `sqrt13+2sqrt13 -> 3sqrt13`