Is a square root of a positive number always an irrational number?

No. The square root of positive integers written in square e.g 4=2² , 9=3², 16=4² and so on is rational. That is sqrt of 4= sqrt of 2²= 2 which is not irrational.

Can a square root be an integer?

The square roots of the perfect squares (e.g., 0, 1, 4, 9, 16) are integers. In all other cases, the square roots of positive integers are irrational numbers, and hence have non-repeating decimals in their decimal representations.

How do you know if a square root is irrational?

If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end (non-terminating) and does not repeat a pattern (non-repeating).

Is square root of 52 rational or irrational?

The square root of 52 is an irrational number.

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

No, the square roots of all positive integers are not irrational. As we can take an example, √4 = ± 2 where 2 and -2 are both rational numbers.

Are square roots of all positive integers irrational if not give an example of the square?

No, the square roots of all positive integers in not irrational. For example √9 = 3, √25 = 5, hence square roots of all positive integers is not irrational. For example, √25 = 5 is rational.

Is square root 4 an integer?

Is the Square Root of 4 Rational or Irrational? A number that can be expressed as a ratio of two integers, i.e., p/q, q = 0 is called a rational number. Thus, √4 is a rational number.

Is square root 1 an integer?

√−1=i is an imaginary number, not lying anywhere on the real number line. Therefore as others have said, it is neither rational nor irrational in the usual senses of those words.

Is square root of 25 rational or irrational?

The square root of 25 is equal to 5 as 25 is a perfect square of 5. Hence, as 5 is a integer and can be expressed in the form of p/q root 25 is rational number.

Is square root of 8 rational or irrational?

Hence, the square root of 8 is not a rational number. It is an irrational number.

Is square root 169 Rational?

Is the Square Root of 169 Rational or Irrational? Both numbers can be represented in the form of a rational number. Hence, the square root of 169 is a rational number.

How do you prove that a number is irrational?

To prove that a number is irrational, show that it is almost rational. Loosely speaking, if you can approximate \\alpha well by rationals, then \\alpha is irrational. This turns out to be a very useful starting point for proofs of irrationality.

Is the square root of 11 rational?

After calculation, we find that 11 is not a perfect square. So, when we calculate the square root which has 11 as a value, it produces 3.23 as a result, which is not a rational number. Therefore we can say that square root of 11 is an irrational number (not a rational number).

Is Pi 2 Irrational?

Pi is an irrational number because it cannot be expressed as a ratio (fraction) of two integers: it has no exact decimal equivalent, although 3.1415926 is good enough for many applications. The square root of 2 is another irrational number that cannot be written as a fraction.