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\sqrt{7+3\times 1+\sqrt{4}}
Calculate the square root of 1 and get 1.
\sqrt{7+3+\sqrt{4}}
Multiply 3 and 1 to get 3.
\sqrt{10+\sqrt{4}}
Add 7 and 3 to get 10.
\sqrt{10+2}
Calculate the square root of 4 and get 2.
\sqrt{12}
Add 10 and 2 to get 12.
2\sqrt{3}
Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.