Solve sqrt{(2sqrt{6})^2-6}

$$\sqrt { ( 2 \sqrt { 6 } ) ^ { 2 } - 6 }$$

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

Solution Steps

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{6} is 6.

$$\sqrt{4\times 6-6}$$

Multiply 4 and 6 to get 24.

$$\sqrt{24-6}$$

Subtract 6 from 24 to get 18.

$$\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$3\sqrt{2}$$