Solve (sqrt{20}-3sqrt{5})*sqrt{40}

$$( \sqrt { 20 } - 3 \sqrt { 5 } ) \cdot \sqrt { 40 }$$

Evaluate

$$-10\sqrt{2}\approx -14.142135624$$

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}.

$$\left(2\sqrt{5}-3\sqrt{5}\right)\sqrt{40}$$

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

$$-\sqrt{5}\sqrt{40}$$

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}.

$$-\sqrt{5}\times 2\sqrt{10}$$

Multiply -1 and 2 to get -2.

$$-2\sqrt{5}\sqrt{10}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$-2\sqrt{5}\sqrt{5}\sqrt{2}$$

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

$$-2\times 5\sqrt{2}$$

Multiply -2 and 5 to get -10.

$$-10\sqrt{2}$$