Yes.
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The square of 36 is 1,296 ... rational.The square root of 36 is 6 ... also rational.
Yes. It's -6 .
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Yes. Both square roots of 36 are rational.
The definition of rational means it can be expressed as a fraction were the top and bottom numbers are whole numbers so the negative square root of 36 (-6) is rational because it can be expressed as a fraction -6/1 or 12/-2 or anything like that. Hoped this helped =)