Solve sqrt{24}*sqrt{54}

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

Evaluate

$$36$$

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}.

$$2\sqrt{6}\sqrt{54}$$

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}.

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

Multiply 2 and 3 to get 6.

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

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

$$6\times 6$$

Multiply 6 and 6 to get 36.

$$36$$

Factor

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