Wellcome!

Question 1. Asked on :19 April 2019:08:21:00 AM

#### Prove that√5 is irrational.

-Added by Prince Rawat Mathematics » Real Number

Himanshi Verma

Let us assume that √5 is rational

Then √5 =

(a and b are co primes, with only 1 common factor and b≠0)

⇒ √5 =

(cross multiply)

⇒ a = √5b

⇒ a² = 5b² -------> α

⇒ 5/a²

(by theorem if p divides q then p can also divide q²)

⇒ 5/a ----> 1

⇒ a = 5c

(squaring on both sides)

⇒ a² = 25c² ----> β

From equations α and β

⇒ 5b² = 25c²

⇒ b² = 5c²

⇒ 5/b²

(again by theorem)

⇒ 5/b---> 2

we know that a and b are co-primes having only 1 common factor but from 1 and 2 we can that it is wrong.

This contradiction arises because we assumed that √5 is a rational number

∴ our assumption is wrong

∴ √5 is irrational number.

-Answered by Himanshi Verma On 21 April 2019:11:24:50 AM(1799Average Rating Based on rating)

You can see here all the solutions of this question by various user for NCERT Solutions. We hope this try will help you in your study and performance.

This Solution may be usefull for your practice and CBSE Exams or All label exams of secondory examination. These solutions or answers are user based solution which may be or not may be by expert but you have to use this at your own understanding of your syllabus.

#### What do you have in your Mind....

* Now You can earn points on every asked question and Answer by you. This points make you a valuable user on this forum. This facility is only available for registered user and educators.

## Search your Question Or Keywords

#### Do you have a question to ask?

User Earned Point: Select

## All Tags by Subjects:

Science (1906)
History (200)
Geography (296)
Economics (157)
Political Science (95)
Mathematics (195)
General Knowledge (5431)
Biology (93)
Physical Education (20)
Chemistry (118)
Civics (114)
Home Science (12)
Sociology (8)
Hindi (43)
English (247)
Physics (1422)
Other (92)
Accountancy (176)