Solve sqrt{(0.2002*46.9512)div(46.9512-25.9176)}

$$\sqrt{ (0.2002 \times 46.9512) \div (46.9512-25.9176) }$$

Evaluate

$$\frac{\sqrt{1751240634}}{62600}\approx 0.668495641$$

Solution Steps

Multiply 0.2002 and 46.9512 to get 9.39963024.

$$\sqrt{\frac{9.39963024}{46.9512-25.9176}}$$

Subtract 25.9176 from 46.9512 to get 21.0336.

$$\sqrt{\frac{9.39963024}{21.0336}}$$

Expand \frac{9.39963024}{21.0336} by multiplying both numerator and the denominator by 100000000.

$$\sqrt{\frac{939963024}{2103360000}}$$

Reduce the fraction \frac{939963024}{2103360000} to lowest terms by extracting and canceling out 336.

$$\sqrt{\frac{2797509}{6260000}}$$

Rewrite the square root of the division \sqrt{\frac{2797509}{6260000}} as the division of square roots \frac{\sqrt{2797509}}{\sqrt{6260000}}.

$$\frac{\sqrt{2797509}}{\sqrt{6260000}}$$

Factor 6260000=100^{2}\times 626. Rewrite the square root of the product \sqrt{100^{2}\times 626} as the product of square roots \sqrt{100^{2}}\sqrt{626}. Take the square root of 100^{2}.

$$\frac{\sqrt{2797509}}{100\sqrt{626}}$$

Rationalize the denominator of \frac{\sqrt{2797509}}{100\sqrt{626}} by multiplying numerator and denominator by \sqrt{626}.

$$\frac{\sqrt{2797509}\sqrt{626}}{100\left(\sqrt{626}\right)^{2}}$$

The square of \sqrt{626} is 626.

$$\frac{\sqrt{2797509}\sqrt{626}}{100\times 626}$$

To multiply \sqrt{2797509} and \sqrt{626}, multiply the numbers under the square root.

$$\frac{\sqrt{1751240634}}{100\times 626}$$

Multiply 100 and 626 to get 62600.

$$\frac{\sqrt{1751240634}}{62600}$$