Solve 250/sqrt{280div25}

$$\frac { 250 } { \sqrt { 280 } \div 25 }$$

Evaluate

$$\frac{625\sqrt{70}}{14}\approx 373.508940417$$

Solution Steps

Divide 250 by \frac{\sqrt{280}}{25} by multiplying 250 by the reciprocal of \frac{\sqrt{280}}{25}.

$$\frac{250\times 25}{\sqrt{280}}$$

Multiply 250 and 25 to get 6250.

$$\frac{6250}{\sqrt{280}}$$

Factor 280=2^{2}\times 70. Rewrite the square root of the product \sqrt{2^{2}\times 70} as the product of square roots \sqrt{2^{2}}\sqrt{70}. Take the square root of 2^{2}.

$$\frac{6250}{2\sqrt{70}}$$

Rationalize the denominator of \frac{6250}{2\sqrt{70}} by multiplying numerator and denominator by \sqrt{70}.

$$\frac{6250\sqrt{70}}{2\left(\sqrt{70}\right)^{2}}$$

The square of \sqrt{70} is 70.

$$\frac{6250\sqrt{70}}{2\times 70}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{625\sqrt{70}}{14}$$