Solve 58.7^2/sqrt{1612}

$$\frac { 58.7 ^ { 2 } } { \sqrt { 1612 } }$$

Evaluate

$$\frac{344569\sqrt{403}}{80600}\approx 85.821022343$$

Solution Steps

Calculate 58.7 to the power of 2 and get 3445.69.

$$\frac{3445.69}{\sqrt{1612}}$$

Factor 1612=2^{2}\times 403. Rewrite the square root of the product \sqrt{2^{2}\times 403} as the product of square roots \sqrt{2^{2}}\sqrt{403}. Take the square root of 2^{2}.

$$\frac{3445.69}{2\sqrt{403}}$$

Rationalize the denominator of \frac{3445.69}{2\sqrt{403}} by multiplying numerator and denominator by \sqrt{403}.

$$\frac{3445.69\sqrt{403}}{2\left(\sqrt{403}\right)^{2}}$$

The square of \sqrt{403} is 403.

$$\frac{3445.69\sqrt{403}}{2\times 403}$$

Multiply 2 and 403 to get 806.

$$\frac{3445.69\sqrt{403}}{806}$$

Divide 3445.69\sqrt{403} by 806 to get \frac{344569}{80600}\sqrt{403}.

$$\frac{344569}{80600}\sqrt{403}$$