Solve 225584/23^2sqrt{2{frac{//}}}

$$\frac{ 225584 }{ { 23 }^{ 2 } \sqrt{ \frac{ 2 }{ \frac{ \frac{ }{ } }{ } } } }$$

Evaluate

$$\frac{4904\sqrt{2}}{23}\approx 301.534926516$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{225584}{23^{2}\sqrt{\frac{2}{\frac{1}{1}}}}$$

Divide 1 by 1 to get 1.

$$\frac{225584}{23^{2}\sqrt{\frac{2}{1}}}$$

Calculate 23 to the power of 2 and get 529.

$$\frac{225584}{529\sqrt{\frac{2}{1}}}$$

Anything divided by one gives itself.

$$\frac{225584}{529\sqrt{2}}$$

Rationalize the denominator of \frac{225584}{529\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{225584\sqrt{2}}{529\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{225584\sqrt{2}}{529\times 2}$$

Cancel out 2\times 23 in both numerator and denominator.

$$\frac{4904\sqrt{2}}{23}$$