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Is square root of 2 a rational number?

  • Last Updated : 03 Sep, 2021

Real numbers that cannot be expressed as a simple fraction are known as irrational numbers. It can’t be represented as a ratio like p/q, where p and q are both integers, q≠0. It’s an inconsistency of rational numbers. Irrational numbers are generally written as R\Q, where the backward slash sign stands for ‘set minus.’ It may also be written as R−Q, which represents the difference between a collection of real and rational numbers.

The computations based on these figures are a little more difficult. Irrational numbers include √5, √11, √21, and so on. If such numbers are utilized in arithmetic operations, the values beneath the root must first be evaluated.

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What are Rational Numbers?

Rational numbers are of the form p/q, where p and q are integers and q ≠ 0. Because of the underlying structure of numbers, p/q form, most individuals find it difficult to distinguish between fractions and rational numbers. When a rational number is divided, the output is in decimal form, which can be either ending or repeating. 3, 4, 5, and so on are some examples of rational numbers as they can be expressed in fraction form as 3/1, 4/1, and 5/1.



What are Irrational Numbers?

Irrational numbers are any numbers that are not rational numbers. Irrational numbers may be represented in decimals but not fractions, which implies they can’t be stated as a ratio of two integers. After the decimal point, irrational numbers have an infinite amount of non-repeating digits.

A real number that cannot be represented as a ratio of integers is called an irrational number. For example, √3 is an irrational number.

An irrational number’s decimal expansion is neither ending nor repeating. The definition of irrational is a number that does not have a ratio or for which no ratio can be stated, i.e, a number that cannot be represented in any other way except by using roots. To put it another way, irrational numbers cannot be expressed as a ratio of two integers.  

Examples of Irrational Numbers

√3, √5, and so on are some examples of irrational numbers as they cannot be expressed in form of p⁄q. Euler’s Number, Golden Ratio, π, and so on are also some examples of irrational numbers. 1/0, 2/0, 3/0, and so on are irrational because they give us unlimited values.

Is √2 a rational number?

Solution:

Irrational numbers are real numbers that cannot be written in the form p/q, where p and q are integers and q≠0. For instance, √3 and √5 and so on are irrational. A rational number is any number that can be written in the form of p/q, where p and q are both integers and q≠0.

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, √2 cannot be expressed in the form of p/q. Alternatively, 2 is a prime number or rational number.  



Here, the given number √2 is equal to 1.4121 which gives the result of non terminating and non recurring decimal, and cannot be expressed as fraction .., so √2 is Irrational Number.

Similar Questions

Question 1: Is √7 a rational number or an irrational number?

Answer:

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, √7 cannot be expressed in the form of p/q. Alternatively, 7 is a prime number. This means that the number 7 has no pair and is not divisible by 2. Hence, √7 is an irrational number.  

Question 2: Determine whether 5.152152…. is a rational number.

Answer:

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, 5.152152…. has recurring digits. Hence, 5.152152…. is a rational number.

Question 3: Is √11 a rational number or an irrational number?

Answer:

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, √11 cannot be expressed in the form of p/q. Alternatively, 11 is a prime number. This means that the number 11 has no pair and is not divisible by 2. Hence, √11 is a irrational number.

Question 4: Determine whether 7.23 is a rational number or an irrational number.

Answer:

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, 7.23…. has terminating digits. Hence, 7.23 is a rational number.

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