Solve (sqrt{125}-sqrt{20})(sqrt[3]{8/27})

$$( \sqrt { 125 } - \sqrt { 20 } ) ( \sqrt[ 3 ] { \frac { 8 } { 27 } } )$$

Evaluate

$$2\sqrt{5}\approx 4.472135955$$

Solution Steps

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\left(5\sqrt{5}-\sqrt{20}\right)\sqrt[3]{\frac{8}{27}}$$

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}.

$$\left(5\sqrt{5}-2\sqrt{5}\right)\sqrt[3]{\frac{8}{27}}$$

Combine 5\sqrt{5} and -2\sqrt{5} to get 3\sqrt{5}.

$$3\sqrt{5}\sqrt[3]{\frac{8}{27}}$$

Calculate \sqrt[3]{\frac{8}{27}} and get \frac{2}{3}.

$$3\sqrt{5}\times \frac{2}{3}$$

Multiply 3 and \frac{2}{3} to get 2.

$$2\sqrt{5}$$