Solve sqrt{4^2+2^2+2^2}

$$\sqrt { 4 ^ { 2 } + 2 ^ { 2 } + 2 ^ { 2 } }$$

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16+2^{2}+2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{16+4+2^{2}}$$

Add 16 and 4 to get 20.

$$\sqrt{20+2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{20+4}$$

Add 20 and 4 to get 24.

$$\sqrt{24}$$

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}.

$$2\sqrt{6}$$