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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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Is the square of 2 rational number?
Yes, the square of any rational number is also a rational number.The square root of 2 is not a rational number.
Is the square root of 4 irrational or 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.
Is the square root of 75 rational or irrational?
The square root of (any number that isn't a perfect square) is irrational.
Is a square root always an irrational number?
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
If you add a rational and irrational number what is the sum?
an irrational number PROOF : Let x be any rational number and y be any irrational number. let us assume that their sum is rational which is ( z ) x + y = z if x is a rational number then ( -x ) will also be a rational number. Therefore, x + y + (-x) = a rational number this implies that y is also rational BUT HERE IS THE CONTRADICTION as we assumed y an irrational number. Hence, our assumption is wrong. This states that x + y is not rational. HENCE PROVEDit will always be irrational.
Is the square of 2 rational number?
Yes, the square of any rational number is also a rational number.The square root of 2 is not a rational number.
Is 2 squared rational or irrational?
The square of any rational number is also rational.
Is the square root of 4 irrational or 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.
IS 0.4 squared an irrational number?
The square of any rational number is also rational.
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.
Is the square root of 14 rational or irrational 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.
Is the square root 1 over square root 4 irrational rational?
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
Is the square root of 133 irrational or rational explain?
It is irrational. 133 = 7*17 and so is not the square of any rational number. Therefore its square root cannot be rational.
Is the square root of 0.0125 a rational number?
a rational number is any number that can be expressed as the quotient or fraction a/b of two integers,yes
Is 6 square root of 26 rational number?
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.
Is the square root of -24 rational?
No. The square root of -24 isn't even real, let alone rational because the square root of any negative number is going to be an imaginary number.
Which square root number is rational?
The square root of any perfect square, or a ratio of perfect squares. eg sqrt(9/25) = 3/5, is rational.
