Evaluate
30\sqrt{3}\approx 51.961524227
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5\times 4\sqrt{3}+2\sqrt{5}\sqrt{15}
Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.
20\sqrt{3}+2\sqrt{5}\sqrt{15}
Multiply 5 and 4 to get 20.
20\sqrt{3}+2\sqrt{5}\sqrt{5}\sqrt{3}
Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.
20\sqrt{3}+2\times 5\sqrt{3}
Multiply \sqrt{5} and \sqrt{5} to get 5.
20\sqrt{3}+10\sqrt{3}
Multiply 2 and 5 to get 10.
30\sqrt{3}
Combine 20\sqrt{3} and 10\sqrt{3} to get 30\sqrt{3}.
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