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\sqrt{5^{2}+\left(5+7\right)^{2}}
Add 1 and 4 to get 5.
\sqrt{25+\left(5+7\right)^{2}}
Calculate 5 to the power of 2 and get 25.
\sqrt{25+12^{2}}
Add 5 and 7 to get 12.
\sqrt{25+144}
Calculate 12 to the power of 2 and get 144.
\sqrt{169}
Add 25 and 144 to get 169.
13
Calculate the square root of 169 and get 13.