Solve sqrt{40}-3sqrt{90}=

$$\sqrt { 40 } - 3 \sqrt { 90 } =$$

Evaluate

$$-7\sqrt{10}\approx -22.135943621$$

Solution Steps

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}.

$$2\sqrt{10}-3\sqrt{90}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

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

Multiply -3 and 3 to get -9.

$$2\sqrt{10}-9\sqrt{10}$$

Combine 2\sqrt{10} and -9\sqrt{10} to get -7\sqrt{10}.

$$-7\sqrt{10}$$