Evaluate
3\sqrt{5}+5\sqrt{3}\approx 15.36845797
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\sqrt{15}\sqrt{3}+\sqrt{15}\sqrt{5}
Use the distributive property to multiply \sqrt{15} by \sqrt{3}+\sqrt{5}.
\sqrt{3}\sqrt{5}\sqrt{3}+\sqrt{15}\sqrt{5}
Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.
3\sqrt{5}+\sqrt{15}\sqrt{5}
Multiply \sqrt{3} and \sqrt{3} to get 3.
3\sqrt{5}+\sqrt{5}\sqrt{3}\sqrt{5}
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}.
3\sqrt{5}+5\sqrt{3}
Multiply \sqrt{5} and \sqrt{5} to get 5.
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