Solve frac{1/7/-4sqrt{3}}{7}

$$\frac { \frac { \frac { 1 } { 7 } } { - 4 \sqrt { 3 } } } { 7 }$$

Evaluate

$$-\frac{\sqrt{3}}{588}\approx -0.002945665$$

Solution Steps

Express \frac{\frac{\frac{1}{7}}{-4\sqrt{3}}}{7} as a single fraction.

$$\frac{\frac{1}{7}}{-4\sqrt{3}\times 7}$$

Multiply -4 and 7 to get -28.

$$\frac{\frac{1}{7}}{-28\sqrt{3}}$$

Express \frac{\frac{1}{7}}{-28\sqrt{3}} as a single fraction.

$$\frac{1}{7\left(-28\right)\sqrt{3}}$$

Rationalize the denominator of \frac{1}{7\left(-28\right)\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3}}{7\left(-28\right)\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{7\left(-28\right)\times 3}$$

Multiply 7 and -28 to get -196.

$$\frac{\sqrt{3}}{-196\times 3}$$

Multiply -196 and 3 to get -588.

$$\frac{\sqrt{3}}{-588}$$