Question

what is the sqrt of 96

Answer 1

or 9.7979

Answer 2

Ah, maybe you're wondering just how to figure this out?

Answer 3

\[\sqrt{96} = \]
You could break 96 down into its prime factorization:
\[96=2*48 = 2*2*24=2*2*2*12\]\[=2*2*2*2*6=2*2*2*2*2*3\]For each pair of identical factors under square root sign, you can move one of them outside of the radical:

\[\sqrt{96} = \sqrt{(2*2)*(2*2)*2*3} = 2*2* \sqrt{2*3}=4\sqrt{6}\]

You could also notice that \(96 = 6*16\), and \(16\) is a perfect square (\(4^2=16)\):
\[\sqrt{96} = \sqrt{6*16} = \sqrt{6}*\sqrt{16} = \sqrt{6}*4 = 4\sqrt{6}\]