Solve sqrt{90}+2sqrt{160}

$$\sqrt{ 90 } +2 \sqrt{ 160 }$$

Evaluate

$$11\sqrt{10}\approx 34.785054262$$

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}.

$$3\sqrt{10}+2\sqrt{160}$$

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}.

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

Multiply 2 and 4 to get 8.

$$3\sqrt{10}+8\sqrt{10}$$

Combine 3\sqrt{10} and 8\sqrt{10} to get 11\sqrt{10}.

$$11\sqrt{10}$$