Solve 6/sqrt{164}

$$\frac{ 6 }{ \sqrt{ 164 } }$$

Evaluate

$$\frac{3\sqrt{41}}{41}\approx 0.468521286$$

Solution Steps

Factor 164=2^{2}\times 41. Rewrite the square root of the product \sqrt{2^{2}\times 41} as the product of square roots \sqrt{2^{2}}\sqrt{41}. Take the square root of 2^{2}.

$$\frac{6}{2\sqrt{41}}$$

Rationalize the denominator of \frac{6}{2\sqrt{41}} by multiplying numerator and denominator by \sqrt{41}.

$$\frac{6\sqrt{41}}{2\left(\sqrt{41}\right)^{2}}$$

The square of \sqrt{41} is 41.

$$\frac{6\sqrt{41}}{2\times 41}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{41}}{41}$$