Solve 5sqrt{13}divsqrt{50}

$$5 \sqrt{ 13 } \div \sqrt{ 50 }$$

Evaluate

$$\frac{\sqrt{26}}{2}\approx 2.549509757$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{5\sqrt{13}}{5\sqrt{2}}$$

Cancel out 5 in both numerator and denominator.

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

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

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

The square of \sqrt{2} is 2.

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

To multiply \sqrt{13} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{26}}{2}$$