Solve (sqrt{40}+sqrt{180})divsqrt[1]{5}

$$( \sqrt { 40 } + \sqrt { 180 } ) \div \sqrt[ 1 ] { 5 }$$

Evaluate

$$\frac{2\left(\sqrt{10}+3\sqrt{5}\right)}{5}\approx 3.948192637$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{2\sqrt{10}+\sqrt{180}}{\sqrt[1]{5}}$$

Factor 180=6^{2}\times 5. Rewrite the square root of the product \sqrt{6^{2}\times 5} as the product of square roots \sqrt{6^{2}}\sqrt{5}. Take the square root of 6^{2}.

$$\frac{2\sqrt{10}+6\sqrt{5}}{\sqrt[1]{5}}$$

Calculate \sqrt[1]{5} and get 5.

$$\frac{2\sqrt{10}+6\sqrt{5}}{5}$$