Solve sqrt{(-2)^2+(-sqrt{6})^2+sqrt{7^2}}

$$\sqrt { ( - 2 ) ^ { 2 } + ( - \sqrt { 6 } ) ^ { 2 } + \sqrt { 7 ^ { 2 } } }$$

Evaluate

$$\sqrt{17}\approx 4.123105626$$

Solution Steps

Calculate -2 to the power of 2 and get 4.

$$\sqrt{4+\left(-\sqrt{6}\right)^{2}+\sqrt{7^{2}}}$$

Calculate -\sqrt{6} to the power of 2 and get \left(\sqrt{6}\right)^{2}.

$$\sqrt{4+\left(\sqrt{6}\right)^{2}+\sqrt{7^{2}}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{4+\left(\sqrt{6}\right)^{2}+\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\sqrt{4+\left(\sqrt{6}\right)^{2}+7}$$

Add 4 and 7 to get 11.

$$\sqrt{11+\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\sqrt{11+6}$$

Add 11 and 6 to get 17.

$$\sqrt{17}$$