Solve 4sqrt{160}+2sqrt{40}

$$4 \sqrt { 160 } + 2 \sqrt { 40 }$$

Evaluate

$$20\sqrt{10}\approx 63.245553203$$

Solution Steps

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}.

$$4\times 4\sqrt{10}+2\sqrt{40}$$

Multiply 4 and 4 to get 16.

$$16\sqrt{10}+2\sqrt{40}$$

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}.

$$16\sqrt{10}+2\times 2\sqrt{10}$$

Multiply 2 and 2 to get 4.

$$16\sqrt{10}+4\sqrt{10}$$

Combine 16\sqrt{10} and 4\sqrt{10} to get 20\sqrt{10}.

$$20\sqrt{10}$$