Question

someone one update me on how to simplify \[\sqrt{216}\], is it 3sqrt{24}?

Answer 1

\[\sqrt{216}\]

Answer 2

is it \[3\sqrt{24}\] is what i meant to type

Answer 3

I would factor the 216 into primes:
it is divisible by 2, so 2*108, 2* 2* 54,
2*2*2*27,
now 27 is divisible by 3 (sum of its digits is div by 3: 2+7= 9)
we get
2*2*2* 3*3*3

find pairs of numbers:
(2*2) (3*3) 2*3
pull the pairs out from the square root
\[ 2\cdot3 \sqrt{2*\cdot3}\]
that simplifies to
\[ 6\sqrt{6} \]

Answer 4

notice you have
3*sqrt(24)
but 24 is 2*2* 6
so you could pull out the 2*2 pair to get
3*2*sqrt(6) or
6 sqrt(6)

Answer 5

perfection, i totally understand now. I needed help on how to do the paring, but now i see whats happening, thank you!

Answer 6

anything that doesnt pair, you have to mulitply it and put it under the radical

Answer 7

yes.

Answer 8

thank you so much