Solve 4sqrt{32}+8sqrt{2}

$$4 \sqrt{ 32 } +8 \sqrt{ 2 }$$

Evaluate

$$24\sqrt{2}\approx 33.941125497$$

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}.

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

Multiply 4 and 4 to get 16.

$$16\sqrt{2}+8\sqrt{2}$$

Combine 16\sqrt{2} and 8\sqrt{2} to get 24\sqrt{2}.

$$24\sqrt{2}$$