Solve sqrt{40}+sqrt{90}+sqrt{250}

$$\sqrt { 40 } + \sqrt { 90 } + \sqrt { 250 }$$

Evaluate

$$10\sqrt{10}\approx 31.622776602$$

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}.

$$2\sqrt{10}+\sqrt{90}+\sqrt{250}$$

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}.

$$2\sqrt{10}+3\sqrt{10}+\sqrt{250}$$

Combine 2\sqrt{10} and 3\sqrt{10} to get 5\sqrt{10}.

$$5\sqrt{10}+\sqrt{250}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$5\sqrt{10}+5\sqrt{10}$$

Combine 5\sqrt{10} and 5\sqrt{10} to get 10\sqrt{10}.

$$10\sqrt{10}$$