Solve sqrt{8}+3sqrt{32}=

$$\sqrt { 8 } + 3 \sqrt { 32 } =$$

Evaluate

$$14\sqrt{2}\approx 19.798989873$$

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}.

$$2\sqrt{2}+3\sqrt{32}$$

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}.

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

Multiply 3 and 4 to get 12.

$$2\sqrt{2}+12\sqrt{2}$$

Combine 2\sqrt{2} and 12\sqrt{2} to get 14\sqrt{2}.

$$14\sqrt{2}$$