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No other way of doing these than simply working it out. I assume the word "rout" means "root", in particular "square root". If not, the following is wrong. sqrt 7 + sqrt 3 = 2.645+ 1.732 = 4.378, sqrt5 + sqrt 5 = 2x2.236=4.472, 2+ sqrt 6 = 2 + 2.449 =4.449 so the middle one wins (better check my arithmetic yourself!)
19
2.82842712
-8
The square root is 238198.4 approx.