Solve sqrt{54}*2sqrt{24}

$$\sqrt{ 54 } \times 2 \sqrt{ 24 }$$

Evaluate

$$72$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$2\times 3\sqrt{6}\sqrt{24}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{6}\sqrt{24}$$

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}.

$$6\sqrt{6}\times 2\sqrt{6}$$

Multiply 6 and 2 to get 12.

$$12\sqrt{6}\sqrt{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$12\times 6$$

Multiply 12 and 6 to get 72.

$$72$$

Factor

$$2^{3}\times 3^{2}$$