Solve (sqrt{20}+sqrt{80})*sqrt{5}

$$( \sqrt { 20 } + \sqrt { 80 } ) \cdot \sqrt { 5 }$$

Evaluate

$$30$$

Solution Steps

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}.

$$\left(2\sqrt{5}+\sqrt{80}\right)\sqrt{5}$$

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}.

$$\left(2\sqrt{5}+4\sqrt{5}\right)\sqrt{5}$$

Combine 2\sqrt{5} and 4\sqrt{5} to get 6\sqrt{5}.

$$6\sqrt{5}\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$6\times 5$$

Multiply 6 and 5 to get 30.

$$30$$

Factor

$$2\times 3\times 5$$