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\sqrt{15^{2}+\left(15-3\right)^{2}}
Add 4 and 11 to get 15.
\sqrt{225+\left(15-3\right)^{2}}
Calculate 15 to the power of 2 and get 225.
\sqrt{225+12^{2}}
Subtract 3 from 15 to get 12.
\sqrt{225+144}
Calculate 12 to the power of 2 and get 144.
\sqrt{369}
Add 225 and 144 to get 369.
3\sqrt{41}
Factor 369=3^{2}\times 41. Rewrite the square root of the product \sqrt{3^{2}\times 41} as the product of square roots \sqrt{3^{2}}\sqrt{41}. Take the square root of 3^{2}.