Solve sqrt{90}+8sqrt{160}

$$\sqrt { 90 } + 8 \sqrt { 160 }$$

Evaluate

$$35\sqrt{10}\approx 110.679718106$$

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}.

$$3\sqrt{10}+8\sqrt{160}$$

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}.

$$3\sqrt{10}+8\times 4\sqrt{10}$$

Multiply 8 and 4 to get 32.

$$3\sqrt{10}+32\sqrt{10}$$

Combine 3\sqrt{10} and 32\sqrt{10} to get 35\sqrt{10}.

$$35\sqrt{10}$$