Solve =628/sqrt{412*1016}

$$= \frac { 628 } { \sqrt { 412 } \times 1016 }$$

Evaluate

$$\frac{157\sqrt{103}}{52324}\approx 0.030452106$$

Solution Steps

Factor 412=2^{2}\times 103. Rewrite the square root of the product \sqrt{2^{2}\times 103} as the product of square roots \sqrt{2^{2}}\sqrt{103}. Take the square root of 2^{2}.

$$\frac{628}{1016\times 2\sqrt{103}}$$

Multiply 1016 and 2 to get 2032.

$$\frac{628}{2032\sqrt{103}}$$

Rationalize the denominator of \frac{628}{2032\sqrt{103}} by multiplying numerator and denominator by \sqrt{103}.

$$\frac{628\sqrt{103}}{2032\left(\sqrt{103}\right)^{2}}$$

The square of \sqrt{103} is 103.

$$\frac{628\sqrt{103}}{2032\times 103}$$

Cancel out 4 in both numerator and denominator.

$$\frac{157\sqrt{103}}{103\times 508}$$

Multiply 103 and 508 to get 52324.

$$\frac{157\sqrt{103}}{52324}$$