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\sqrt{21+75}
Subtract 27 from 48 to get 21.
\sqrt{96}
Add 21 and 75 to get 96.
4\sqrt{6}
Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.