Solve sqrt{12^2+(2sqrt{6})^2}

$$\sqrt { 12 ^ { 2 } + ( 2 \sqrt { 6 } ) ^ { 2 } }$$

Evaluate

$$2\sqrt{42}\approx 12.961481397$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\sqrt{144+\left(2\sqrt{6}\right)^{2}}$$

Expand \left(2\sqrt{6}\right)^{2}.

$$\sqrt{144+2^{2}\left(\sqrt{6}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{144+4\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\sqrt{144+4\times 6}$$

Multiply 4 and 6 to get 24.

$$\sqrt{144+24}$$

Add 144 and 24 to get 168.

$$\sqrt{168}$$

Factor 168=2^{2}\times 42. Rewrite the square root of the product \sqrt{2^{2}\times 42} as the product of square roots \sqrt{2^{2}}\sqrt{42}. Take the square root of 2^{2}.

$$2\sqrt{42}$$