No. The square root of most numbers is irrational - only if the number of which you take the root happen to be perfect squares, do you get a rational root. In this case, to take the square root of 3/4, 3 is not a perfect square, so the root is not rational. Or you can take .75 to be 75/100; once again, 75 is not a perfect square, so the root is irrational.
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is the square root of 3 rational
No, the square root of 1500 is not a rational number.
The square root of 225 is 15, which is a rational number.
Only if the square root of the numerator and the square root of the denominator are both rational numbers.
The square root of 75 = 8.660254030.....