Evaluate
2\sqrt{3}\approx 3.464101615
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\sqrt{3}\sqrt{15}-3\sqrt{3}+\sqrt{5}\sqrt{15}-3\sqrt{5}
Apply the distributive property by multiplying each term of \sqrt{3}+\sqrt{5} by each term of \sqrt{15}-3.
\sqrt{3}\sqrt{3}\sqrt{5}-3\sqrt{3}+\sqrt{5}\sqrt{15}-3\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}-3\sqrt{3}+\sqrt{5}\sqrt{15}-3\sqrt{5}
Multiply \sqrt{3} and \sqrt{3} to get 3.
3\sqrt{5}-3\sqrt{3}+\sqrt{5}\sqrt{5}\sqrt{3}-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}-3\sqrt{3}+5\sqrt{3}-3\sqrt{5}
Multiply \sqrt{5} and \sqrt{5} to get 5.
3\sqrt{5}+2\sqrt{3}-3\sqrt{5}
Combine -3\sqrt{3} and 5\sqrt{3} to get 2\sqrt{3}.
2\sqrt{3}
Combine 3\sqrt{5} and -3\sqrt{5} to get 0.
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