Solve 2sqrt{10}-3sqrt{8}*sqrt{20}

$$2 \sqrt { 10 } - 3 \sqrt { 8 } \times \sqrt { 20 }$$

Evaluate

$$-10\sqrt{10}\approx -31.622776602$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{10}-3\times 2\sqrt{2}\sqrt{20}$$

Multiply 3 and 2 to get 6.

$$2\sqrt{10}-6\sqrt{2}\sqrt{20}$$

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}.

$$2\sqrt{10}-6\sqrt{2}\times 2\sqrt{5}$$

Multiply 6 and 2 to get 12.

$$2\sqrt{10}-12\sqrt{2}\sqrt{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$2\sqrt{10}-12\sqrt{10}$$

Combine 2\sqrt{10} and -12\sqrt{10} to get -10\sqrt{10}.

$$-10\sqrt{10}$$