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\sqrt{144+8^{2}+5^{2}}
Calculate 12 to the power of 2 and get 144.
\sqrt{144+64+5^{2}}
Calculate 8 to the power of 2 and get 64.
\sqrt{208+5^{2}}
Add 144 and 64 to get 208.
\sqrt{208+25}
Calculate 5 to the power of 2 and get 25.
\sqrt{233}
Add 208 and 25 to get 233.