Question

What is `sqrt72 - sqrt18`?

Answer 1

`3sqrt2`

Explanation:

72 and 18 are not square numbers so they do not have rational square roots.
Write them as the product of their factors first, use square numbers if possible.

`sqrt72 - sqrt18`

= `sqrt(9xx4xx2) - sqrt (9xx2)`

=`3xx2sqrt2 - 3sqrt2`

= `6sqrt2 - 3sqrt2`

=`3sqrt2`

Answer 2

`3sqrt2`.

Explanation:

Since `(ab)^m=a^m*b^m, and, (c^p)^q=c^(pq)`, we have,

`sqrt72=72^(1/2)=(36*2)^(1/2)=(36^(1/2))(2^(1/2))=((6^2)^(1/2))2^(1/2)`

`=(6^(2*1/2))2^(1/2)=6sqrt2`.

On the same lines, `sqrt18=3sqrt2`.

Therefore, `sqrt72-sqrt18=6sqrt2-3sqrt2=3sqrt2`.