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Q: Is the square of a rational number always greater than the number?
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Does there exist an irrational number such that its square root is rational?

No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).


Is the square of -8 a rational number?

The square of a negative number is always positive. The square of -8 = 64, a rational number


Is the square of a number irrational Always sometimes never?

The square of a rational number can be either rational or irrational. However, the square of an irrational number is always irrational.


Is a square number always a rational number?

Yes


Are the square roots of all positive integers irrational If not give an example of the square root of a number that is a rational number?

The square root of any positive square number is always rational as for example the square root of 36 is 6 which is a rational number.


If x is a rational number is square root of x always irrational?

No. If 'x' is a perfect square, then its square root is also rational.


Is the square of an irrational number always rational?

No. An example of this is pi.


Which counterexample shows the conjecture is falseConjecture: The square of a rational number is greater than or equal to the number.?

A+


Is the square root of a whole number always rational number?

No. More frequently it is not.


Is the square of a number is always greater than the number?

no


A short note on square root of rational number?

Square root of a rational number may either be rational or irrational. For example 1/4 is a rational number whose square root is 1/2. Similarly, 4 is 4/1 which is rational and the square root is 2 which of course is also rational. However, 1/2 and 2 are rational, but their square roots are irrational. We can say the square root of a rational number is always a real number. We can also say the rational numbers whose square roots are also rational are perfect squares or fractions involving perfect squares.


Is the square root of 85 a rational number?

No. The square root of an integer is always either an integer or an irrational number.