Solve frac{sqrt{13}}{sqrt{52}}

$$\frac{ \sqrt{ 13 } }{ \sqrt{ 52 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

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}.

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

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

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

The square of \sqrt{13} is 13.

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

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

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

Multiply 2 and 13 to get 26.

$$\frac{13}{26}$$

Reduce the fraction \frac{13}{26} to lowest terms by extracting and canceling out 13.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$