Solve 4sqrt{2}*3sqrt{24}

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

Evaluate

$$48\sqrt{3}\approx 83.138438763$$

Solution Steps

Factor 24=2\times 12. Rewrite the square root of the product \sqrt{2\times 12} as the product of square roots \sqrt{2}\sqrt{12}.

$$3\times 4\sqrt{2}\sqrt{2}\sqrt{12}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$3\times 4\times 2\sqrt{12}$$

Multiply 3 and 4 to get 12.

$$12\times 2\sqrt{12}$$

Multiply 12 and 2 to get 24.

$$24\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply 24 and 2 to get 48.

$$48\sqrt{3}$$