Solve 215/321*sqrt{252*2}

$$\frac{ 215 }{ 321 \times \sqrt{ 252 \times 2 } }$$

Evaluate

$$\frac{215\sqrt{14}}{26964}\approx 0.029834458$$

Solution Steps

Multiply 252 and 2 to get 504.

$$\frac{215}{321\sqrt{504}}$$

Factor 504=6^{2}\times 14. Rewrite the square root of the product \sqrt{6^{2}\times 14} as the product of square roots \sqrt{6^{2}}\sqrt{14}. Take the square root of 6^{2}.

$$\frac{215}{321\times 6\sqrt{14}}$$

Multiply 321 and 6 to get 1926.

$$\frac{215}{1926\sqrt{14}}$$

Rationalize the denominator of \frac{215}{1926\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{215\sqrt{14}}{1926\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{215\sqrt{14}}{1926\times 14}$$

Multiply 1926 and 14 to get 26964.

$$\frac{215\sqrt{14}}{26964}$$