Solve 3sqrt{32}+2sqrt{8}

$$3 \sqrt { 32 } + 2 \sqrt { 8 }$$

Evaluate

$$16\sqrt{2}\approx 22.627416998$$

Solution Steps

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}.

$$3\times 4\sqrt{2}+2\sqrt{8}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{2}+2\sqrt{8}$$

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}.

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

Multiply 2 and 2 to get 4.

$$12\sqrt{2}+4\sqrt{2}$$

Combine 12\sqrt{2} and 4\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}$$