Solve frac{sqrt{8}}{sqrt{29}}

$$\frac { \sqrt { 8 } } { \sqrt { 29 } }$$

Evaluate

$$\frac{2\sqrt{58}}{29}\approx 0.525225731$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2}}{\sqrt{29}}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.

$$\frac{2\sqrt{2}\sqrt{29}}{\left(\sqrt{29}\right)^{2}}$$

The square of \sqrt{29} is 29.

$$\frac{2\sqrt{2}\sqrt{29}}{29}$$

To multiply \sqrt{2} and \sqrt{29}, multiply the numbers under the square root.

$$\frac{2\sqrt{58}}{29}$$