Solve sqrt{1000}-2sqrt{40}

$$\sqrt { 1000 } - 2 \sqrt { 40 }$$

Evaluate

$$6\sqrt{10}\approx 18.973665961$$

Solution Steps

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$10\sqrt{10}-2\sqrt{40}$$

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}.

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

Multiply -2 and 2 to get -4.

$$10\sqrt{10}-4\sqrt{10}$$

Combine 10\sqrt{10} and -4\sqrt{10} to get 6\sqrt{10}.

$$6\sqrt{10}$$