Solve 6/sqrt{12^2-6^2}

$$\frac{ 6 }{ \sqrt{ { 12 }^{ 2 } - { 6 }^{ 2 } } }$$

Evaluate

$$\frac{\sqrt{3}}{3}\approx 0.577350269$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\frac{6}{\sqrt{144-6^{2}}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{6}{\sqrt{144-36}}$$

Subtract 36 from 144 to get 108.

$$\frac{6}{\sqrt{108}}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$\frac{6}{6\sqrt{3}}$$

Rationalize the denominator of \frac{6}{6\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{6\sqrt{3}}{6\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{6\sqrt{3}}{6\times 3}$$

Cancel out 6 in both numerator and denominator.

$$\frac{\sqrt{3}}{3}$$