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\sqrt{100+25^{2}}
Calculate 10 to the power of 2 and get 100.
\sqrt{100+625}
Calculate 25 to the power of 2 and get 625.
\sqrt{725}
Add 100 and 625 to get 725.
5\sqrt{29}
Factor 725=5^{2}\times 29. Rewrite the square root of the product \sqrt{5^{2}\times 29} as the product of square roots \sqrt{5^{2}}\sqrt{29}. Take the square root of 5^{2}.