Solve sqrt{1000}-sqrt{90}-sqrt{160}

$$\sqrt { 1000 } - \sqrt { 90 } - \sqrt { 160 }$$

Evaluate

$$3\sqrt{10}\approx 9.486832981$$

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}.

$$10\sqrt{10}-\sqrt{90}-\sqrt{160}$$

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}.

$$10\sqrt{10}-3\sqrt{10}-\sqrt{160}$$

Combine 10\sqrt{10} and -3\sqrt{10} to get 7\sqrt{10}.

$$7\sqrt{10}-\sqrt{160}$$

Factor 160=4^{2}\times 10. Rewrite the square root of the product \sqrt{4^{2}\times 10} as the product of square roots \sqrt{4^{2}}\sqrt{10}. Take the square root of 4^{2}.

$$7\sqrt{10}-4\sqrt{10}$$

Combine 7\sqrt{10} and -4\sqrt{10} to get 3\sqrt{10}.

$$3\sqrt{10}$$