Solve 1000divfrac{9sqrt{41}}{41}

$$1000 \div \frac { 9 \sqrt { 41 } } { 41 }$$

Evaluate

$$\frac{1000\sqrt{41}}{9}\approx 711.458248604$$

Solution Steps

Divide 1000 by \frac{9\sqrt{41}}{41} by multiplying 1000 by the reciprocal of \frac{9\sqrt{41}}{41}.

$$\frac{1000\times 41}{9\sqrt{41}}$$

Multiply 1000 and 41 to get 41000.

$$\frac{41000}{9\sqrt{41}}$$

Rationalize the denominator of \frac{41000}{9\sqrt{41}} by multiplying numerator and denominator by \sqrt{41}.

$$\frac{41000\sqrt{41}}{9\left(\sqrt{41}\right)^{2}}$$

The square of \sqrt{41} is 41.

$$\frac{41000\sqrt{41}}{9\times 41}$$

Cancel out 41 in both numerator and denominator.

$$\frac{1000\sqrt{41}}{9}$$