Evaluate
\frac{3\left(\sqrt{5}+10\right)}{2}\approx 18.354101966
Factor
\frac{3 {(\sqrt{5} + 10)}}{2} = 18.354101966249686
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3\left(\sqrt{5}\right)^{2}+\sqrt{5}\left(-\frac{1}{2}\right)+\sqrt{20}
Use the distributive property to multiply \sqrt{5} by 3\sqrt{5}-\frac{1}{2}.
3\times 5+\sqrt{5}\left(-\frac{1}{2}\right)+\sqrt{20}
The square of \sqrt{5} is 5.
15+\sqrt{5}\left(-\frac{1}{2}\right)+\sqrt{20}
Multiply 3 and 5 to get 15.
15+\sqrt{5}\left(-\frac{1}{2}\right)+2\sqrt{5}
Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.
15+\frac{3}{2}\sqrt{5}
Combine \sqrt{5}\left(-\frac{1}{2}\right) and 2\sqrt{5} to get \frac{3}{2}\sqrt{5}.
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