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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.

Q: 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?

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They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.

No. For example, 20.5 is irrational; indeed it was one of the first irrational numbers to be discovered.

Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.

No. For example, pi is a real number, but it is irrational (it cannot be converted into an exact fraction).The reverse is true, however: all rational numbers are also real numbers.

These are called "rational numbers" (ratio -> rational), and can be represented by the set Q (integers are Z, natural numbers are N, real numbers are R, complex numbers are C). Any number that can be expressed as a fraction is a rational number. For example, 0.01 is a rational number, because it can be expressed as 1/100. Irrational numbers are often square roots of non-perfect squares (such as the square root of 2 or 7, but not 4 or 9).

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All integers are rational numbers. There are integers with an i behind them that are imaginary numbers. They are not real numbers but they are rational. The square root of 2 is irrational. It is real but irrational.

Rational. It can be written as a fraction where the denominator is not equal to 0. For example as -17/1. All integers are rational.

All integers are rational, since they can be written, for example, in the form 45/1.

No- integers are a kind of rational number and are not irrational. One well-known example of an irrational number is the square root of 2.

Yes. Both the additive inverse and the multiplicative inverse would be irrational in this case. For example, if a and b are integers, a/b is rational by definition; in this case, b/a would also be rational, being the ratio of two integers.

If the positive square root (for example, square root of 2) is irrational, then the corresponding negative square root (for example, minus square root of 2) is also irrational.

No, they are not because fractions can be negative also. fractions aren't integers

Sure; for example, 10 + pi is irrational, 10 - pi is irrational. Both are positive. If you add them, you get 20.

A number is a rational number when it can be expressed as a fraction otherwise it is an irrational number * * * * * A fraction, in this context, being a ratio of two integers (not pi/2, for example).

Rational. Any number that is the ratio of two integers is by definition rational. For example, -2/3 is the ratio of -2 to 3.Answer 1irrational

They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number.

It isn't always possible to determine. For example, it is unknown whether the Euler-Mascheroni constant (0.5772156649...) is rational or irrational.Most famous numbers and constants are known to be rational or irrational. If it can be expressed as a fraction a/b where a and b are integers, it's rational.