Solve 4sqrt{24}+sqrt{96}

$$4 \sqrt { 24 } + \sqrt { 96 }$$

Evaluate

$$12\sqrt{6}\approx 29.393876913$$

Solution Steps

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}.

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

Multiply 4 and 2 to get 8.

$$8\sqrt{6}+\sqrt{96}$$

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}.

$$8\sqrt{6}+4\sqrt{6}$$

Combine 8\sqrt{6} and 4\sqrt{6} to get 12\sqrt{6}.

$$12\sqrt{6}$$