Solve 22/7*75/2*sqrt{6850/4}

$$\frac{ 22 }{ 7 } \times \frac{ 75 }{ 2 } \times \sqrt{ \frac{ 6850 }{ 4 } }$$

Evaluate

$$\frac{4125\sqrt{274}}{14}\approx 4877.207114189$$

Solution Steps

Multiply \frac{22}{7} times \frac{75}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 75}{7\times 2}\sqrt{\frac{6850}{4}}$$

Do the multiplications in the fraction \frac{22\times 75}{7\times 2}.

$$\frac{1650}{14}\sqrt{\frac{6850}{4}}$$

Reduce the fraction \frac{1650}{14} to lowest terms by extracting and canceling out 2.

$$\frac{825}{7}\sqrt{\frac{6850}{4}}$$

Reduce the fraction \frac{6850}{4} to lowest terms by extracting and canceling out 2.

$$\frac{825}{7}\sqrt{\frac{3425}{2}}$$

Rewrite the square root of the division \sqrt{\frac{3425}{2}} as the division of square roots \frac{\sqrt{3425}}{\sqrt{2}}.

$$\frac{825}{7}\times \frac{\sqrt{3425}}{\sqrt{2}}$$

Factor 3425=5^{2}\times 137. Rewrite the square root of the product \sqrt{5^{2}\times 137} as the product of square roots \sqrt{5^{2}}\sqrt{137}. Take the square root of 5^{2}.

$$\frac{825}{7}\times \frac{5\sqrt{137}}{\sqrt{2}}$$

Rationalize the denominator of \frac{5\sqrt{137}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{825}{7}\times \frac{5\sqrt{137}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{825}{7}\times \frac{5\sqrt{137}\sqrt{2}}{2}$$

To multiply \sqrt{137} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{825}{7}\times \frac{5\sqrt{274}}{2}$$

Multiply \frac{825}{7} times \frac{5\sqrt{274}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{825\times 5\sqrt{274}}{7\times 2}$$

Multiply 825 and 5 to get 4125.

$$\frac{4125\sqrt{274}}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$\frac{4125\sqrt{274}}{14}$$