Solve 44/sqrt{116*sqrt{51}}=

$$\frac { 44 } { \sqrt { 116 } \cdot \sqrt { 51 } } =$$

Evaluate

$$\frac{22\sqrt{1479}}{1479}\approx 0.572056064$$

Solution Steps

Factor 116=2^{2}\times 29. Rewrite the square root of the product \sqrt{2^{2}\times 29} as the product of square roots \sqrt{2^{2}}\sqrt{29}. Take the square root of 2^{2}.

$$\frac{44}{2\sqrt{29}\sqrt{51}}$$

To multiply \sqrt{29} and \sqrt{51}, multiply the numbers under the square root.

$$\frac{44}{2\sqrt{1479}}$$

Rationalize the denominator of \frac{44}{2\sqrt{1479}} by multiplying numerator and denominator by \sqrt{1479}.

$$\frac{44\sqrt{1479}}{2\left(\sqrt{1479}\right)^{2}}$$

The square of \sqrt{1479} is 1479.

$$\frac{44\sqrt{1479}}{2\times 1479}$$

Cancel out 2 in both numerator and denominator.

$$\frac{22\sqrt{1479}}{1479}$$