Solve frac{sqrt{54}*sqrt{6}}{sqrt{3}}

$$\frac { \sqrt { 54 } \times \sqrt { 6 } } { \sqrt { 3 } }$$

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

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}.

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

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

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

Calculate the square root of 9 and get 3.

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

Multiply 6 and 3 to get 18.

$$\frac{18}{\sqrt{3}}$$

Rationalize the denominator of \frac{18}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{18\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{18\sqrt{3}}{3}$$

Divide 18\sqrt{3} by 3 to get 6\sqrt{3}.

$$6\sqrt{3}$$