Solve 3sqrt{32}+sqrt{24}

$$3 \sqrt{ 32 } + \sqrt{ 24 }$$

Evaluate

$$2\sqrt{6}\left(2\sqrt{3}+1\right)\approx 21.869542234$$

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}.

$$3\times 4\sqrt{2}+\sqrt{24}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{2}+\sqrt{24}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$12\sqrt{2}+2\sqrt{6}$$