Solve frac{sqrt{sqrt{144}+sqrt{144}}}{sqrt{36}}

$$\frac { \sqrt { \sqrt { 144 } + \sqrt { 144 } } } { \sqrt { 36 } }$$

Evaluate

$$\frac{\sqrt{6}}{3}\approx 0.816496581$$

Solution Steps

Calculate the square root of 144 and get 12.

$$\frac{\sqrt{12+\sqrt{144}}}{\sqrt{36}}$$

Calculate the square root of 144 and get 12.

$$\frac{\sqrt{12+12}}{\sqrt{36}}$$

Add 12 and 12 to get 24.

$$\frac{\sqrt{24}}{\sqrt{36}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{2\sqrt{6}}{\sqrt{36}}$$

Calculate the square root of 36 and get 6.

$$\frac{2\sqrt{6}}{6}$$

Divide 2\sqrt{6} by 6 to get \frac{1}{3}\sqrt{6}.

$$\frac{1}{3}\sqrt{6}$$