Solve 1sqrt{8}+sqrt{32}

$$1 \sqrt { 8 } + \sqrt { 32 }$$

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$1\times 2\sqrt{2}+\sqrt{32}$$

Multiply 1 and 2 to get 2.

$$2\sqrt{2}+\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

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

$$6\sqrt{2}$$