Solve =sqrt{660/635*1560/1450}

$$= \sqrt { \frac { 660 } { 635 } \times \frac { 1560 } { 1450 } }$$

Evaluate

$$\frac{12\sqrt{2633345}}{18415}\approx 1.057458672$$

Solution Steps

Reduce the fraction \frac{660}{635} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{132}{127}\times \frac{1560}{1450}}$$

Reduce the fraction \frac{1560}{1450} to lowest terms by extracting and canceling out 10.

$$\sqrt{\frac{132}{127}\times \frac{156}{145}}$$

Multiply \frac{132}{127} times \frac{156}{145} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{132\times 156}{127\times 145}}$$

Do the multiplications in the fraction \frac{132\times 156}{127\times 145}.

$$\sqrt{\frac{20592}{18415}}$$

Rewrite the square root of the division \sqrt{\frac{20592}{18415}} as the division of square roots \frac{\sqrt{20592}}{\sqrt{18415}}.

$$\frac{\sqrt{20592}}{\sqrt{18415}}$$

Factor 20592=12^{2}\times 143. Rewrite the square root of the product \sqrt{12^{2}\times 143} as the product of square roots \sqrt{12^{2}}\sqrt{143}. Take the square root of 12^{2}.

$$\frac{12\sqrt{143}}{\sqrt{18415}}$$

Rationalize the denominator of \frac{12\sqrt{143}}{\sqrt{18415}} by multiplying numerator and denominator by \sqrt{18415}.

$$\frac{12\sqrt{143}\sqrt{18415}}{\left(\sqrt{18415}\right)^{2}}$$

The square of \sqrt{18415} is 18415.

$$\frac{12\sqrt{143}\sqrt{18415}}{18415}$$

To multiply \sqrt{143} and \sqrt{18415}, multiply the numbers under the square root.

$$\frac{12\sqrt{2633345}}{18415}$$