Solve sqrt{2*1725div3.14}

$$\sqrt{ 2 \times 1725 \div 3.14 }$$

Evaluate

$$\frac{50\sqrt{10833}}{157}\approx 33.147037796$$

Solution Steps

Multiply 2 and 1725 to get 3450.

$$\sqrt{\frac{3450}{3.14}}$$

Expand \frac{3450}{3.14} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{345000}{314}}$$

Reduce the fraction \frac{345000}{314} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{172500}{157}}$$

Rewrite the square root of the division \sqrt{\frac{172500}{157}} as the division of square roots \frac{\sqrt{172500}}{\sqrt{157}}.

$$\frac{\sqrt{172500}}{\sqrt{157}}$$

Factor 172500=50^{2}\times 69. Rewrite the square root of the product \sqrt{50^{2}\times 69} as the product of square roots \sqrt{50^{2}}\sqrt{69}. Take the square root of 50^{2}.

$$\frac{50\sqrt{69}}{\sqrt{157}}$$

Rationalize the denominator of \frac{50\sqrt{69}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{50\sqrt{69}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{50\sqrt{69}\sqrt{157}}{157}$$

To multiply \sqrt{69} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{50\sqrt{10833}}{157}$$