Question 937768

I do my home work on khanacademy.org and I am doing Pythagorean Theorem. It keeps giving me problems that show a right triangle with two side lengths and I have to find the third length and answer it like this, for example: {{{ 2*sqrt(13) }}} It shows me how I got it wrong but I don't understand how they get the answer so they gave me a triangle that has one leg as "a", another as 5, and the hypotenuse as 9. I put it into an equation of {{{ a^2 + 25 = 81 }}} and then subtracted 25 from both sides and got {{{ a = sqrt (56) }}} and then I did the factor tree with the square root of 56 and had 2 * 24 and then from 24 I had 2 * 12 and then from 12 I had 2 * 6 and from 6 I had 3 * 2. After that I put the answer in as {{{ 2*sqrt (24) }}} but it said it was wrong and told me the answer was {{{ 2* sqrt(14) }}} but I don't understand how they got that and also why that is the answer. Please help me understand and thank you for your using your time to help me.
<pre>When you got: {{{sqrt(56)}}}, and you factored 56 by using the factor tree, you needed to find factors of 56, that
INCLUDES its LARGEST PERFECT SQUARE. That is: 4 * 14, since 4 is the LARGEST PERFECT SQUARE FACTOR of 56.
{{{sqrt(56)}}} now becomes: {{{sqrt(4 * 14)}}}, and when SEPARATED becomes: {{{sqrt(4)}}}{{{"*"}}}{{{sqrt(14)}}}, and finally: {{{highlight_green(2sqrt(14))}}}