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Subjects>Math>Math & Arithmetic

Why are all square roots not irrational numbers?

Anonymous

∙ 7y ago

Updated: 9/26/2023

Because some of them are squares of rational numbers. So their square roots are the rational numbers.Thus if x is rational, then the square roots of x2, which are -x and +x are both rational.

Wiki User

∙ 7y ago

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More answers

because some of them simplify by being the "perfect" squares of smaller numbers. So √225 is not irrational because 225 = 15*15, so √225 = 15 which is not irrational

Wiki User

∙ 7y ago

If you square a rational number (for example, 4/3, which has the square 16/9), then when you take the square root of the result you will of course get your original rational number back.

Wiki User

∙ 7y ago

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Q: Why are all square roots not irrational numbers?

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Continue Learning about Math & Arithmetic

Are all square roots are irrational numbers?

No. The square roots of perfect squares are rational.

Are all square roots irrational?

No.

Why is square root 31 irrational?

In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals.The square root of 31 is one such.

What kind of number system is a square root?

A square root is not a number system. Square roots of non-negative numbers may be rational or irrational, but they all belong to the set of real numbers. The square roots of negative numbers do not. To include them, the number system needs to be extended to the complex numbers.

Are irrational numbers used to find square roots?

All prime numbers have irrational number square roots, so if you try to find the square root of a non-perfect square number use them to simplify it. For example, ±√125 = ±√25*5 = ±5√5 (when you want to show both the square roots) √72 = √36*2 = 6√2 √-27 = √-9*3 = 3i√3

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Related Questions

Are all square roots of even numbers rational?

No. The square roots 8 are irrational, as are the square roots of most even numbers.

Are all square roots are irrational numbers?

No. The square roots of perfect squares are rational.

Are all square roots irrational numbers?

No. Square root of 9=3. 3=3/1. Therefore not all square roots are irrational

What are non recurring irrational numbers?

All irrational numbers are non-recurring. If a number is recurring, it is rational. Examples of irrational numbers include the square root of 2, most square roots, most cubic roots, most 4th. roots, etc., pi, e, and most calculations involving irrational numbers.

Is the square root of 13 irrational or rational?

The square root of 13 is irrational. All square roots of whole numbers are irrational unless the number is a perfect square.

Are irrational numbers square roots?

Usually they are. More specifically, if you take the square root of a positive integer, there are only two possibilities:* If you take the square root of a perfect square, you get a whole number. * In all other cases, you get an irrational number.

What are ten irrational numbers?

The square roots of 2, 3, 5, 6, 7. In all cases there are two roots (+ and -).

Are all square roots irrational?

No.

Is the square root of 19 a rational number?

No. 19 is a prime number, and all prime numbers have irrational roots.

Why is square root 31 irrational?

In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals.The square root of 31 is one such.

What kind of number system is a square root?

A square root is not a number system. Square roots of non-negative numbers may be rational or irrational, but they all belong to the set of real numbers. The square roots of negative numbers do not. To include them, the number system needs to be extended to the complex numbers.

Are irrational numbers used to find square roots?

All prime numbers have irrational number square roots, so if you try to find the square root of a non-perfect square number use them to simplify it. For example, ±√125 = ±√25*5 = ±5√5 (when you want to show both the square roots) √72 = √36*2 = 6√2 √-27 = √-9*3 = 3i√3

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