Solve frac{sqrt{7}}{sqrt{343}}

$$\frac { \sqrt { 7 } } { \sqrt { 343 } }$$

Evaluate

$$\frac{1}{7}\approx 0.142857143$$

Solution Steps

Factor 343=7^{2}\times 7. Rewrite the square root of the product \sqrt{7^{2}\times 7} as the product of square roots \sqrt{7^{2}}\sqrt{7}. Take the square root of 7^{2}.

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

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

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

The square of \sqrt{7} is 7.

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

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

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

Multiply 7 and 7 to get 49.

$$\frac{7}{49}$$

Reduce the fraction \frac{7}{49} to lowest terms by extracting and canceling out 7.

$$\frac{1}{7}$$

Factor

$$\frac{1}{7} = 0.14285714285714285$$