Solve 1/sqrt{6sqrt{26}}

$$\frac{ 1 }{ \sqrt{ 6 } \sqrt{ 26 } }$$

Evaluate

$$\frac{\sqrt{39}}{78}\approx 0.080064077$$

Solution Steps

To multiply \sqrt{6} and \sqrt{26}, multiply the numbers under the square root.

$$\frac{1}{\sqrt{156}}$$

Rationalize the denominator of \frac{1}{\sqrt{156}} by multiplying numerator and denominator by \sqrt{156}.

$$\frac{\sqrt{156}}{\left(\sqrt{156}\right)^{2}}$$

The square of \sqrt{156} is 156.

$$\frac{\sqrt{156}}{156}$$

Factor 156=2^{2}\times 39. Rewrite the square root of the product \sqrt{2^{2}\times 39} as the product of square roots \sqrt{2^{2}}\sqrt{39}. Take the square root of 2^{2}.

$$\frac{2\sqrt{39}}{156}$$

Divide 2\sqrt{39} by 156 to get \frac{1}{78}\sqrt{39}.

$$\frac{1}{78}\sqrt{39}$$