Solve 2sqrt{8}+5sqrt{32}

$$2 \sqrt { 8 } + 5 \sqrt { 32 }$$

Evaluate

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

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}.

$$2\times 2\sqrt{2}+5\sqrt{32}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{2}+5\sqrt{32}$$

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}.

$$4\sqrt{2}+5\times 4\sqrt{2}$$

Multiply 5 and 4 to get 20.

$$4\sqrt{2}+20\sqrt{2}$$

Combine 4\sqrt{2} and 20\sqrt{2} to get 24\sqrt{2}.

$$24\sqrt{2}$$