Solve frac{sqrt{7}}{sqrt{700}}

$$\frac { \sqrt { 7 } } { \sqrt { 700 } }$$

Evaluate

$$\frac{1}{10}=0.1$$

Solution Steps

Factor 700=10^{2}\times 7. Rewrite the square root of the product \sqrt{10^{2}\times 7} as the product of square roots \sqrt{10^{2}}\sqrt{7}. Take the square root of 10^{2}.

$$\frac{\sqrt{7}}{10\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{7}}{10\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{7}\sqrt{7}}{10\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{7}\sqrt{7}}{10\times 7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{7}{10\times 7}$$

Multiply 10 and 7 to get 70.

$$\frac{7}{70}$$

Reduce the fraction \frac{7}{70} to lowest terms by extracting and canceling out 7.

$$\frac{1}{10}$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$