Solve frac{sqrt{91}}{sqrt{52}}

$$\frac { \sqrt { 91 } } { \sqrt { 52 } }$$

Evaluate

$$\frac{\sqrt{7}}{2}\approx 1.322875656$$

Solution Steps

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$\frac{\sqrt{91}}{2\sqrt{13}}$$

Rationalize the denominator of \frac{\sqrt{91}}{2\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\sqrt{91}\sqrt{13}}{2\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{\sqrt{91}\sqrt{13}}{2\times 13}$$

Factor 91=13\times 7. Rewrite the square root of the product \sqrt{13\times 7} as the product of square roots \sqrt{13}\sqrt{7}.

$$\frac{\sqrt{13}\sqrt{7}\sqrt{13}}{2\times 13}$$

Multiply \sqrt{13} and \sqrt{13} to get 13.

$$\frac{13\sqrt{7}}{2\times 13}$$

Multiply 2 and 13 to get 26.

$$\frac{13\sqrt{7}}{26}$$

Divide 13\sqrt{7} by 26 to get \frac{1}{2}\sqrt{7}.

$$\frac{1}{2}\sqrt{7}$$