Solve 1/sqrt{14sqrt{27}}

$$\frac{ 1 }{ \sqrt{ 14 } \sqrt{ 27 } }$$

Evaluate

$$\frac{\sqrt{42}}{126}\approx 0.05143445$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{1}{\sqrt{14}\times 3\sqrt{3}}$$

To multiply \sqrt{14} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{1}{\sqrt{42}\times 3}$$

Rationalize the denominator of \frac{1}{\sqrt{42}\times 3} by multiplying numerator and denominator by \sqrt{42}.

$$\frac{\sqrt{42}}{\left(\sqrt{42}\right)^{2}\times 3}$$

The square of \sqrt{42} is 42.

$$\frac{\sqrt{42}}{42\times 3}$$

Multiply 42 and 3 to get 126.

$$\frac{\sqrt{42}}{126}$$