Question

Help Check my answer? (algebra)(will fan/medal) Please help.
The question: http://i.imgur.com/KnYORKL.jpg
My answer: http://i.imgur.com/nZEKEpL.jpg

Answer 1

if you know a number is a "perfect square" e.g. 81 = 9*9
then you can take its square root.
so I would do
\[ \frac{\sqrt{216}}{9} \]
I don't know about 216, so I start by factoring it. I know 2 divides into it (because it's even)
(I know 4 does because if 4 divides evenly into the last 2 digits (16 here) 4 divides into the whole number 216)
any way, we get
4 * 54
if the sum of the digits are div by 3 (5+4 =9) then so is the whole number:
ditto if the sum is div by 9: 5+4 =9, so 54 is div by 9:
4 * 9* 6
and 6 is 2*3
we can take the square root of 4 * 9
we get 2*3
and we are left with sqr(6)
finally
\[ \frac{2\cdot 3}{9} \sqrt{6} = \frac{2}{3} \sqrt{6} \]

Answer 2

Thank you sooo much, you're a lifesaver! <3