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Find an irrational number between 3 and 4

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  • Difficulty Level : Basic
  • Last Updated : 06 Aug, 2021
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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. 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.

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

√2, √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.

Find an irrational number between 3 and 4

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, √2 and √3 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.

Here, the given numbers are 3 and 4. There can be an infinite number of irrational numbers between these numbers. The numbers between the squares of 3 and 4, i.e., between 9 and 16 are 10, 11, …14, 15. The square root of any of these numbers is always an irrational number. The square root of 10, i.e., √10 is an irrational number that lies between 3 and 4.

Similar Questions

Question 1: What is the irrational number between 4 and 5?

Solution:

Here, the given numbers are 4 and 5. The numbers between the squares of 4 and 5, i.e., between 16 and 25 are 17, 18, …23, 24. The square root of any of these numbers is always an irrational number. The square root of 19, i.e., √19 is an irrational number that lies between 4 and 5.

Question 2: What is the irrational number between 5 and 6?

Solution:

Here, the given numbers are 5 and 6. The numbers between the squares of 5 and 6, i.e., between 25 and 36 are 26, 27, …34, 35. The square root of any of these numbers is always an irrational number. The square root of 27, i.e., √27 is an irrational number that lies between 5 and 6.

Question 3: What is the irrational number between 1 and 2?

Solution:

Here, the given numbers are 1 and 2. The numbers between the squares of 1 and 2, i.e., between 1 and 4 are 2 and 3. The square root of any of these numbers is always an irrational number. The square root of 3, i.e., √3 is an irrational number that lies between 1 and 2.

Question 4: What is the irrational number between -1 and 3?

Solution:

Here, the given numbers are -1 and 3. The square root of 2, i.e., √2 is an irrational number that lies between -1 and 3.

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