Solve sqrt{962.5/frac{22{7}}}

$$\sqrt{ \frac{ 962.5 }{ \frac{ 22 }{ 7 } } }$$

Evaluate

$$17.5$$

Solution Steps

Divide 962.5 by \frac{22}{7} by multiplying 962.5 by the reciprocal of \frac{22}{7}.

$$\sqrt{962.5\times \frac{7}{22}}$$

Convert decimal number 962.5 to fraction \frac{9625}{10}. Reduce the fraction \frac{9625}{10} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{1925}{2}\times \frac{7}{22}}$$

Multiply \frac{1925}{2} times \frac{7}{22} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{1925\times 7}{2\times 22}}$$

Do the multiplications in the fraction \frac{1925\times 7}{2\times 22}.

$$\sqrt{\frac{13475}{44}}$$

Reduce the fraction \frac{13475}{44} to lowest terms by extracting and canceling out 11.

$$\sqrt{\frac{1225}{4}}$$

Rewrite the square root of the division \frac{1225}{4} as the division of square roots \frac{\sqrt{1225}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{35}{2}$$

Factor

$$\frac{5 \cdot 7}{2} = 17\frac{1}{2} = 17.5$$