Solve sqrt{54div55}

$$\sqrt{ 54 \div 55 }$$

Evaluate

$$\frac{3\sqrt{330}}{55}\approx 0.990867389$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{54}{55}} as the division of square roots \frac{\sqrt{54}}{\sqrt{55}}.

$$\frac{\sqrt{54}}{\sqrt{55}}$$

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}.

$$\frac{3\sqrt{6}}{\sqrt{55}}$$

Rationalize the denominator of \frac{3\sqrt{6}}{\sqrt{55}} by multiplying numerator and denominator by \sqrt{55}.

$$\frac{3\sqrt{6}\sqrt{55}}{\left(\sqrt{55}\right)^{2}}$$

The square of \sqrt{55} is 55.

$$\frac{3\sqrt{6}\sqrt{55}}{55}$$

To multiply \sqrt{6} and \sqrt{55}, multiply the numbers under the square root.

$$\frac{3\sqrt{330}}{55}$$