Solve 26divsqrt{52}

$$26 \div \sqrt{ 52 }$$

Evaluate

$$\sqrt{13}\approx 3.605551275$$

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}.

$$\frac{26}{2\sqrt{13}}$$

Rationalize the denominator of \frac{26}{2\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{26\sqrt{13}}{2\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{26\sqrt{13}}{2\times 13}$$

Cancel out 2\times 13 in both numerator and denominator.

$$\sqrt{13}$$