Solve 1/sqrt{117}

$$\frac{ 1 }{ \sqrt{ 117 } }$$

Evaluate

$$\frac{\sqrt{13}}{39}\approx 0.092450033$$

Solution Steps

Factor 117=3^{2}\times 13. Rewrite the square root of the product \sqrt{3^{2}\times 13} as the product of square roots \sqrt{3^{2}}\sqrt{13}. Take the square root of 3^{2}.

$$\frac{1}{3\sqrt{13}}$$

Rationalize the denominator of \frac{1}{3\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\sqrt{13}}{3\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{\sqrt{13}}{3\times 13}$$

Multiply 3 and 13 to get 39.

$$\frac{\sqrt{13}}{39}$$