Solve 4sqrt{72}+4sqrt{128}-sqrt{96}

$$4 \sqrt { 72 } + 4 \sqrt { 128 } - \sqrt { 96 }$$

Evaluate

$$56\sqrt{2}-4\sqrt{6}\approx 69.398000522$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$4\times 6\sqrt{2}+4\sqrt{128}-\sqrt{96}$$

Multiply 4 and 6 to get 24.

$$24\sqrt{2}+4\sqrt{128}-\sqrt{96}$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$24\sqrt{2}+4\times 8\sqrt{2}-\sqrt{96}$$

Multiply 4 and 8 to get 32.

$$24\sqrt{2}+32\sqrt{2}-\sqrt{96}$$

Combine 24\sqrt{2} and 32\sqrt{2} to get 56\sqrt{2}.

$$56\sqrt{2}-\sqrt{96}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$56\sqrt{2}-4\sqrt{6}$$