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.
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.
Yes, the square of any rational number is also a rational number.The square root of 2 is not a rational number.
A non-square rational number is a rational number that cannot be expressed as the square of any rational number. For example, ( \frac{2}{3} ) is a non-square rational number because there are no rational numbers whose square equals ( \frac{2}{3} ). In general, any rational number that does not have a perfect square as its numerator and denominator is considered a non-square rational.
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 of any rational number is also rational.
The square of any rational number is also rational.
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.
Search for the proof for the irrationality of the square root of 2. The same reasoning applies to any positive integer that is not a perfect square. In summary, the square root of any positive integer is either a whole number, or - as in this case - it is irrational.
Yes because any number that can be expressed as a fraction is a rational number and the answer in the question is 1/2 which is rational
It is irrational. 133 = 7*17 and so is not the square of any rational number. Therefore its square root cannot be rational.
a rational number is any number that can be expressed as the quotient or fraction a/b of two integers,yes
It is irrational. * The square root of any positive integer, except of a perfect square, is irrational. * The product of an irrational number and a rational number (except zero) is irrational.
Yes, the square root of 25 is a rational number. A rational number is any number that can be expressed as a fraction of two integers. The square root of 25 is 5, which can be expressed as the fraction 5/1. Therefore, 5 is a rational number.