Solve sqrt{10}-sqrt{32}+sqrt{90}

$$\sqrt { 10 } - \sqrt { 32 } + \sqrt { 90 }$$

Evaluate

$$4\left(\sqrt{10}-\sqrt{2}\right)\approx 6.992256391$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\sqrt{10}-4\sqrt{2}+\sqrt{90}$$

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}.

$$\sqrt{10}-4\sqrt{2}+3\sqrt{10}$$

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

$$4\sqrt{10}-4\sqrt{2}$$