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
Well, isn't that just a happy little fact! You see, when you square a rational number, you're just multiplying it by itself. Since multiplying two rational numbers always gives you another rational number, the square of any rational number will also be rational. Just like painting a beautiful landscape, math can be full of wonderful patterns and harmonious relationships.