• February 12th 2011, 01:32 AM
alyosha2
$
\sqrt{8x^5y^6} = \sqrt{4x^4y^62x}
$

why $2x$?

why not

$\sqrt{8x^5y^6} = \sqrt{8x^4y^6x}$

?
• February 12th 2011, 01:34 AM
Moo
Because 4 is a square while 8 isn't :)
• February 12th 2011, 01:57 AM
alyosha2
I mean why factor the 8 out at this point? The odd exponent has been factored out of the x to make it even. I understand that at some point the 8 will have to be factored, but is it just pure subjctive preference that it has been pulled out here rather than doing it later? or does it have some thing to do with making the x's exponent even?
• February 12th 2011, 02:11 AM
Prove It
Because you're looking for square factors, so that you can take square roots...