Question

How do you find 2 sqrt 325?

Answer 1

Assuming we are dealing with only the principal square root:
`color(white)("XXX")2sqrt(325)=10sqrt(13)`
Using a calculator we could further evaluate this as `36.05551`

Explanation:

`325 = 5xx5xx13`

So
`color(white)("XXX")sqrt(325) = sqrt(5^2xx13) = sqrt(5^2)*sqrt(13) = 5sqrt(13)`
and
`color(white)("XXX")2sqrt(325) =2xx5sqrt(13)=10sqrt(13)`

The simplest way to find an approximation for the irrational value `sqrt(13)` is to use a calculator.

If we are not restricted to the principal square root then `-10sqrt(13)` is another solution.