# Thread: Sanity Check

1. ## Sanity Check

My son has a question on a school paper which goes as follows

Simplify

$\sqrt{\left ( 15p \right )^{2}-\left ( 9k \right )^{2}}$

Maybe I am losing it, but this does not seem like it can be simplified. If the minus was a times then ok, but not like this.

2. ## Re: Sanity Check

Originally Posted by grillage
My son has a question on a school paper which goes as follows

Simplify

$\sqrt{\left ( 15p \right )^{2}-\left ( 9k \right )^{2}}$
you can do one small thing

$\sqrt{\left ( 15p \right )^{2}-\left ( 9k \right )^{2}}$

$\sqrt{3^2\cdot 25p^2 - 3^2\cdot 9k^2}$

$3\sqrt{25p^2-9k^2}$

3. ## Re: Sanity Check

Thanks, but I still suspect that they intended a multiplication.

4. ## Re: Sanity Check

you can factor it to become

$3\sqrt{(5p-3k)(5p+3k)}$

I don't know that I'd call that any simpler.

5. ## Re: Sanity Check

Hello, grillage!

Sanity Check

My son has a question on a school paper which goes as follows:

Simplify: . $\sqrt{\left ( 15p \right )^{2}-\left ( 9k \right )^{2}}$

Maybe I am losing it, but this does not seem like it can be simplified.
If the minus was a times, then ok, but not like this.

It can be simplifed as romsek suggested.

Your son could invoke the Sanity Clause that excuses him from the problem.

But, of course, there isn't any Sanity Clause.