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\sqrt{4+2^{2}}
Calculate 2 to the power of 2 and get 4.
\sqrt{4+4}
Calculate 2 to the power of 2 and get 4.
\sqrt{8}
Add 4 and 4 to get 8.
2\sqrt{2}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.