Solve sqrt{3250*16/3.14*21}

$$\sqrt{ \frac{ 3250 \times 16 }{ 3.14 \times 21 } }$$

Evaluate

$$\frac{200\sqrt{214305}}{3297}\approx 28.081946034$$

Solution Steps

Multiply 3250 and 16 to get 52000.

$$\sqrt{\frac{52000}{3.14\times 21}}$$

Multiply 3.14 and 21 to get 65.94.

$$\sqrt{\frac{52000}{65.94}}$$

Expand \frac{52000}{65.94} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{5200000}{6594}}$$

Reduce the fraction \frac{5200000}{6594} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{2600000}{3297}}$$

Rewrite the square root of the division \sqrt{\frac{2600000}{3297}} as the division of square roots \frac{\sqrt{2600000}}{\sqrt{3297}}.

$$\frac{\sqrt{2600000}}{\sqrt{3297}}$$

Factor 2600000=200^{2}\times 65. Rewrite the square root of the product \sqrt{200^{2}\times 65} as the product of square roots \sqrt{200^{2}}\sqrt{65}. Take the square root of 200^{2}.

$$\frac{200\sqrt{65}}{\sqrt{3297}}$$

Rationalize the denominator of \frac{200\sqrt{65}}{\sqrt{3297}} by multiplying numerator and denominator by \sqrt{3297}.

$$\frac{200\sqrt{65}\sqrt{3297}}{\left(\sqrt{3297}\right)^{2}}$$

The square of \sqrt{3297} is 3297.

$$\frac{200\sqrt{65}\sqrt{3297}}{3297}$$

To multiply \sqrt{65} and \sqrt{3297}, multiply the numbers under the square root.

$$\frac{200\sqrt{214305}}{3297}$$