Irrational
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It is irrational. 133 = 7*17 and so is not the square of any rational number. Therefore its square root cannot be rational.
11.5326
11.532562594670795889354183238818 round to whatever decimal you want.
Well, honey, 133 can be equal to a lot of things. It could be 66 + 67, or 133 divided by 1. Or if you're feeling fancy, it could be the square root of 17689. Math is full of surprises, darling.
133 square yards = 1,197 square feet.