The square root of 172 is 13.114877. it is really hard to figure out (almost imnpossible) without a calculator
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162 is 256 and 172 is 289, so YES, √266 is irrational
172 is a not perfect square.
sqrt(172) = 17 ==========just bring the 17 our from under the radical as it is shown factored under the radical
There are infinitely many of them. They include square root of (4.41) square root of (4.42) square root of (4.43) square root of (4.44) square root of (4.45) square root of (5.3) square root of (5.762) square root of (6) square root of (6.1) square root of (6.2)