Solve (sqrt{20}-sqrt{30})sqrt{5}

$$( \sqrt { 20 } - \sqrt { 30 } ) \sqrt { 5 }$$

Evaluate

$$10-5\sqrt{6}\approx -2.247448714$$

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}.

$$\left(2\sqrt{5}-\sqrt{30}\right)\sqrt{5}$$

Use the distributive property to multiply 2\sqrt{5}-\sqrt{30} by \sqrt{5}.

$$2\left(\sqrt{5}\right)^{2}-\sqrt{30}\sqrt{5}$$

The square of \sqrt{5} is 5.

$$2\times 5-\sqrt{30}\sqrt{5}$$

Multiply 2 and 5 to get 10.

$$10-\sqrt{30}\sqrt{5}$$

Factor 30=5\times 6. Rewrite the square root of the product \sqrt{5\times 6} as the product of square roots \sqrt{5}\sqrt{6}.

$$10-\sqrt{5}\sqrt{6}\sqrt{5}$$

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

$$10-5\sqrt{6}$$