Solve 22/7*7.5/2*sqrt{68.50/4}

$$\frac{ 22 }{ 7 } \times \frac{ 7.5 }{ 2 } \times \sqrt{ \frac{ 68.50 }{ 4 } }$$

Evaluate

$$\frac{165\sqrt{274}}{56}\approx 48.772071142$$

Solution Steps

Expand \frac{7.5}{2} by multiplying both numerator and the denominator by 10.

$$\frac{22}{7}\times \frac{75}{20}\sqrt{\frac{68.5}{4}}$$

Reduce the fraction \frac{75}{20} to lowest terms by extracting and canceling out 5.

$$\frac{22}{7}\times \frac{15}{4}\sqrt{\frac{68.5}{4}}$$

Multiply \frac{22}{7} times \frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 15}{7\times 4}\sqrt{\frac{68.5}{4}}$$

Do the multiplications in the fraction \frac{22\times 15}{7\times 4}.

$$\frac{330}{28}\sqrt{\frac{68.5}{4}}$$

Reduce the fraction \frac{330}{28} to lowest terms by extracting and canceling out 2.

$$\frac{165}{14}\sqrt{\frac{68.5}{4}}$$

Expand \frac{68.5}{4} by multiplying both numerator and the denominator by 10.

$$\frac{165}{14}\sqrt{\frac{685}{40}}$$

Reduce the fraction \frac{685}{40} to lowest terms by extracting and canceling out 5.

$$\frac{165}{14}\sqrt{\frac{137}{8}}$$

Rewrite the square root of the division \sqrt{\frac{137}{8}} as the division of square roots \frac{\sqrt{137}}{\sqrt{8}}.

$$\frac{165}{14}\times \frac{\sqrt{137}}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{165}{14}\times \frac{\sqrt{137}}{2\sqrt{2}}$$

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

$$\frac{165}{14}\times \frac{\sqrt{137}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{165}{14}\times \frac{\sqrt{137}\sqrt{2}}{2\times 2}$$

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

$$\frac{165}{14}\times \frac{\sqrt{274}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{165}{14}\times \frac{\sqrt{274}}{4}$$

Multiply \frac{165}{14} times \frac{\sqrt{274}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{165\sqrt{274}}{14\times 4}$$

Multiply 14 and 4 to get 56.

$$\frac{165\sqrt{274}}{56}$$