Solve frac{sqrt{49}}{3}divfrac{sqrt{108}}{6}

$$\frac{ \sqrt{ 49 } }{ 3 } \div \frac{ \sqrt{ 108 } }{ 6 }$$

Evaluate

$$\frac{7\sqrt{3}}{9}\approx 1.347150628$$

Solution Steps

Divide \frac{\sqrt{49}}{3} by \frac{\sqrt{108}}{6} by multiplying \frac{\sqrt{49}}{3} by the reciprocal of \frac{\sqrt{108}}{6}.

$$\frac{\sqrt{49}\times 6}{3\sqrt{108}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\sqrt{49}}{\sqrt{108}}$$

Calculate the square root of 49 and get 7.

$$\frac{2\times 7}{\sqrt{108}}$$

Multiply 2 and 7 to get 14.

$$\frac{14}{\sqrt{108}}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$\frac{14}{6\sqrt{3}}$$

Rationalize the denominator of \frac{14}{6\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{14\sqrt{3}}{6\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{14\sqrt{3}}{6\times 3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{7\sqrt{3}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{7\sqrt{3}}{9}$$