Solve sqrt{1592/1124*2036/1438*100}

$$\sqrt { \frac { 1592 } { 1124 } \times \frac { 2036 } { 1438 } \times 100 }$$

Evaluate

$$\frac{20\sqrt{20464732349}}{202039}\approx 14.161127073$$

Solution Steps

Reduce the fraction \frac{1592}{1124} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{398}{281}\times \frac{2036}{1438}\times 100}$$

Reduce the fraction \frac{2036}{1438} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{398}{281}\times \frac{1018}{719}\times 100}$$

Multiply \frac{398}{281} times \frac{1018}{719} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{398\times 1018}{281\times 719}\times 100}$$

Do the multiplications in the fraction \frac{398\times 1018}{281\times 719}.

$$\sqrt{\frac{405164}{202039}\times 100}$$

Express \frac{405164}{202039}\times 100 as a single fraction.

$$\sqrt{\frac{405164\times 100}{202039}}$$

Multiply 405164 and 100 to get 40516400.

$$\sqrt{\frac{40516400}{202039}}$$

Rewrite the square root of the division \sqrt{\frac{40516400}{202039}} as the division of square roots \frac{\sqrt{40516400}}{\sqrt{202039}}.

$$\frac{\sqrt{40516400}}{\sqrt{202039}}$$

Factor 40516400=20^{2}\times 101291. Rewrite the square root of the product \sqrt{20^{2}\times 101291} as the product of square roots \sqrt{20^{2}}\sqrt{101291}. Take the square root of 20^{2}.

$$\frac{20\sqrt{101291}}{\sqrt{202039}}$$

Rationalize the denominator of \frac{20\sqrt{101291}}{\sqrt{202039}} by multiplying numerator and denominator by \sqrt{202039}.

$$\frac{20\sqrt{101291}\sqrt{202039}}{\left(\sqrt{202039}\right)^{2}}$$

The square of \sqrt{202039} is 202039.

$$\frac{20\sqrt{101291}\sqrt{202039}}{202039}$$

To multiply \sqrt{101291} and \sqrt{202039}, multiply the numbers under the square root.

$$\frac{20\sqrt{20464732349}}{202039}$$