Solve frac{sqrt{66}}{sqrt{54}}

$$\frac { \sqrt { 66 } } { \sqrt { 54 } }$$

Evaluate

$$\frac{\sqrt{11}}{3}\approx 1.105541597$$

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}.

$$\frac{\sqrt{66}}{3\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{66}}{3\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{66}\sqrt{6}}{3\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{66}\sqrt{6}}{3\times 6}$$

Factor 66=6\times 11. Rewrite the square root of the product \sqrt{6\times 11} as the product of square roots \sqrt{6}\sqrt{11}.

$$\frac{\sqrt{6}\sqrt{11}\sqrt{6}}{3\times 6}$$

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

$$\frac{6\sqrt{11}}{3\times 6}$$

Multiply 3 and 6 to get 18.

$$\frac{6\sqrt{11}}{18}$$

Divide 6\sqrt{11} by 18 to get \frac{1}{3}\sqrt{11}.

$$\frac{1}{3}\sqrt{11}$$