Solve =frac{sqrt{1004}}{sqrt{1035}}

$$= \frac { \sqrt { 1004 } } { \sqrt { 1035 } }$$

Evaluate

$$\frac{2\sqrt{28865}}{345}\approx 0.984910305$$

Solution Steps

Factor 1004=2^{2}\times 251. Rewrite the square root of the product \sqrt{2^{2}\times 251} as the product of square roots \sqrt{2^{2}}\sqrt{251}. Take the square root of 2^{2}.

$$\frac{2\sqrt{251}}{\sqrt{1035}}$$

Factor 1035=3^{2}\times 115. Rewrite the square root of the product \sqrt{3^{2}\times 115} as the product of square roots \sqrt{3^{2}}\sqrt{115}. Take the square root of 3^{2}.

$$\frac{2\sqrt{251}}{3\sqrt{115}}$$

Rationalize the denominator of \frac{2\sqrt{251}}{3\sqrt{115}} by multiplying numerator and denominator by \sqrt{115}.

$$\frac{2\sqrt{251}\sqrt{115}}{3\left(\sqrt{115}\right)^{2}}$$

The square of \sqrt{115} is 115.

$$\frac{2\sqrt{251}\sqrt{115}}{3\times 115}$$

To multiply \sqrt{251} and \sqrt{115}, multiply the numbers under the square root.

$$\frac{2\sqrt{28865}}{3\times 115}$$

Multiply 3 and 115 to get 345.

$$\frac{2\sqrt{28865}}{345}$$