Solve sqrt{40}+sqrt{160}

$$\sqrt{ 40 } + \sqrt{ 160 }$$

Evaluate

$$6\sqrt{10}\approx 18.973665961$$

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}.

$$2\sqrt{10}+\sqrt{160}$$

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}.

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

Combine 2\sqrt{10} and 4\sqrt{10} to get 6\sqrt{10}.

$$6\sqrt{10}$$