Solve sqrt{90}-sqrt{40}

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

Evaluate

$$\sqrt{10}\approx 3.16227766$$

Solution Steps

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}.

$$3\sqrt{10}-\sqrt{40}$$

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}.

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

Combine 3\sqrt{10} and -2\sqrt{10} to get \sqrt{10}.

$$\sqrt{10}$$