Consider a rational number, p.
p is rational so p = x/y where x and y are integers.
x is an integer so x*x is an integer, and y is an integer so y*y is an integer.
So p2 = (x/y)2 = x2/y2 is a ratio of two integers and so is rational.
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Yes, the square of any rational number is also a rational number.The square root of 2 is not a rational number.
It is rational. The root of a perfect square, such as 4, is rational; the root of any positive integer that is not a perfect square is an irrational number.
The square root of (any number that isn't a perfect square) is irrational.
No; the square root of any rational number squared is that rational number. Examples: √(2^2) = √4 = 2. √((1/2)^2) = √(1/4) = 1/2
A rational number can be expressed as a fraction of two integers. When you square a rational number, you are essentially multiplying it by itself. Since the product of two integers is also an integer, the square of any rational number will also be a rational number. This is because the result can be expressed as a fraction of two integers, making it rational.