Solve sqrt{48510/3.14*35}=

$$\sqrt{ \frac{ 48510 }{ 3.14 \times 35 } } =$$

Evaluate

$$\frac{30\sqrt{12089}}{157}\approx 21.009551968$$

Solution Steps

Multiply 3.14 and 35 to get 109.9.

$$\sqrt{\frac{48510}{109.9}}$$

Expand \frac{48510}{109.9} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{485100}{1099}}$$

Reduce the fraction \frac{485100}{1099} to lowest terms by extracting and canceling out 7.

$$\sqrt{\frac{69300}{157}}$$

Rewrite the square root of the division \sqrt{\frac{69300}{157}} as the division of square roots \frac{\sqrt{69300}}{\sqrt{157}}.

$$\frac{\sqrt{69300}}{\sqrt{157}}$$

Factor 69300=30^{2}\times 77. Rewrite the square root of the product \sqrt{30^{2}\times 77} as the product of square roots \sqrt{30^{2}}\sqrt{77}. Take the square root of 30^{2}.

$$\frac{30\sqrt{77}}{\sqrt{157}}$$

Rationalize the denominator of \frac{30\sqrt{77}}{\sqrt{157}} by multiplying numerator and denominator by \sqrt{157}.

$$\frac{30\sqrt{77}\sqrt{157}}{\left(\sqrt{157}\right)^{2}}$$

The square of \sqrt{157} is 157.

$$\frac{30\sqrt{77}\sqrt{157}}{157}$$

To multiply \sqrt{77} and \sqrt{157}, multiply the numbers under the square root.

$$\frac{30\sqrt{12089}}{157}$$