Solve sqrt{80}-(sqrt{20}-5sqrt{1/5})

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Quiz

Arithmetic

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4\sqrt{5}-\left(\sqrt{20}-5\sqrt{\frac{1}{5}}\right)

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

4\sqrt{5}-\left(2\sqrt{5}-5\sqrt{\frac{1}{5}}\right)

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}.

4\sqrt{5}-\left(2\sqrt{5}-5\times \frac{\sqrt{1}}{\sqrt{5}}\right)

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

4\sqrt{5}-\left(2\sqrt{5}-5\times \frac{1}{\sqrt{5}}\right)

Calculate the square root of 1 and get 1.

4\sqrt{5}-\left(2\sqrt{5}-5\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

4\sqrt{5}-\left(2\sqrt{5}-5\times \frac{\sqrt{5}}{5}\right)

The square of \sqrt{5} is 5.

4\sqrt{5}-\left(2\sqrt{5}-\sqrt{5}\right)

Cancel out 5 and 5.

4\sqrt{5}-\sqrt{5}

Combine 2\sqrt{5} and -\sqrt{5} to get \sqrt{5}.