Solve 4/3sqrt{6}*sqrt{54}

$$\frac { 4 } { 3 } \sqrt { 6 } \cdot \sqrt { 54 }$$

Evaluate

$$24$$

Solution Steps

Factor 54=6\times 9. Rewrite the square root of the product \sqrt{6\times 9} as the product of square roots \sqrt{6}\sqrt{9}.

$$\frac{4}{3}\sqrt{6}\sqrt{6}\sqrt{9}$$

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

$$\frac{4}{3}\times 6\sqrt{9}$$

Express \frac{4}{3}\times 6 as a single fraction.

$$\frac{4\times 6}{3}\sqrt{9}$$

Multiply 4 and 6 to get 24.

$$\frac{24}{3}\sqrt{9}$$

Divide 24 by 3 to get 8.

$$8\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$8\times 3$$

Multiply 8 and 3 to get 24.

$$24$$

Factor

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