Question

What is the simplest radical form of `sqrt160`?

Answer 1

`4sqrt10`

Explanation:

Write 160 as the product of its prime factors, then we know what we are dealing with.

`sqrt160 = sqrt(2xx2xx2xx2xx2xx2xx5) = sqrt(2^5 xx 5)`

=`sqrt(2^5 xx 5) = sqrt(2^4 xx 2 xx 5)`

=`4sqrt10`

Answer 2

Radicals can be split by multiplication. It helps to be able to find perfect squares underneath the radicals during the factorization, and `16` is a convenient perfect square.

If it helps, try going in steps of factoring out `2`.

`sqrt(160)`

`sqrt(2*80)`

`sqrt(2*2*40)`

`sqrt(2*2*2*20)`

`sqrt(2*2*2*2*10)`

`= sqrt(16*10)`

`= sqrt(16)*sqrt(10)`

Since `sqrt(16) = 4`, we end up with `color(blue)(4sqrt10)`.