Solve 40.50div(sqrt{(15927.96div100)}

$$40.50 \div ( \sqrt{ (15927.96 \div 100) }$$

Evaluate

$$\frac{675\sqrt{398199}}{132733}\approx 3.209038629$$

Solution Steps

Expand \frac{15927.96}{100} by multiplying both numerator and the denominator by 100.

$$\frac{40.5}{\sqrt{\frac{1592796}{10000}}}$$

Reduce the fraction \frac{1592796}{10000} to lowest terms by extracting and canceling out 4.

$$\frac{40.5}{\sqrt{\frac{398199}{2500}}}$$

Rewrite the square root of the division \sqrt{\frac{398199}{2500}} as the division of square roots \frac{\sqrt{398199}}{\sqrt{2500}}.

$$\frac{40.5}{\frac{\sqrt{398199}}{\sqrt{2500}}}$$

Calculate the square root of 2500 and get 50.

$$\frac{40.5}{\frac{\sqrt{398199}}{50}}$$

Divide 40.5 by \frac{\sqrt{398199}}{50} by multiplying 40.5 by the reciprocal of \frac{\sqrt{398199}}{50}.

$$\frac{40.5\times 50}{\sqrt{398199}}$$

Rationalize the denominator of \frac{40.5\times 50}{\sqrt{398199}} by multiplying numerator and denominator by \sqrt{398199}.

$$\frac{40.5\times 50\sqrt{398199}}{\left(\sqrt{398199}\right)^{2}}$$

The square of \sqrt{398199} is 398199.

$$\frac{40.5\times 50\sqrt{398199}}{398199}$$

Multiply 40.5 and 50 to get 2025.

$$\frac{2025\sqrt{398199}}{398199}$$

Divide 2025\sqrt{398199} by 398199 to get \frac{675}{132733}\sqrt{398199}.

$$\frac{675}{132733}\sqrt{398199}$$