Solve sqrt{2.648/2166*3016/2500}

$$\sqrt { \frac { 2.648 } { 2166 } \times \frac { 3016 } { 2500 } }$$

Evaluate

$$\frac{\sqrt{1871805}}{35625}\approx 0.038403909$$

Solution Steps

Expand \frac{2.648}{2166} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{2648}{2166000}\times \frac{3016}{2500}}$$

Reduce the fraction \frac{2648}{2166000} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{331}{270750}\times \frac{3016}{2500}}$$

Reduce the fraction \frac{3016}{2500} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{331}{270750}\times \frac{754}{625}}$$

Multiply \frac{331}{270750} times \frac{754}{625} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{331\times 754}{270750\times 625}}$$

Do the multiplications in the fraction \frac{331\times 754}{270750\times 625}.

$$\sqrt{\frac{249574}{169218750}}$$

Reduce the fraction \frac{249574}{169218750} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{124787}{84609375}}$$

Rewrite the square root of the division \sqrt{\frac{124787}{84609375}} as the division of square roots \frac{\sqrt{124787}}{\sqrt{84609375}}.

$$\frac{\sqrt{124787}}{\sqrt{84609375}}$$

Factor 84609375=2375^{2}\times 15. Rewrite the square root of the product \sqrt{2375^{2}\times 15} as the product of square roots \sqrt{2375^{2}}\sqrt{15}. Take the square root of 2375^{2}.

$$\frac{\sqrt{124787}}{2375\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{124787}}{2375\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{124787}\sqrt{15}}{2375\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{124787}\sqrt{15}}{2375\times 15}$$

To multiply \sqrt{124787} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{1871805}}{2375\times 15}$$

Multiply 2375 and 15 to get 35625.

$$\frac{\sqrt{1871805}}{35625}$$