CBSE Class 10CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for Prove that the Following is Irrational 1 √ 2 - CBSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

Prove that the following is irrational

`1/sqrt2`

Solution

`1/sqrt2`

`1/sqrt2 xx sqrt2/sqrt2 = sqrt2/2`

Let a = `(1/2)sqrt2` be a rational number

⇒ 2a = `sqrt2`

2a is a rational number since product of two rational number is a rational number.

Which will imply that `sqrt2` is a rational number. But it is a contradiciton since `sqrt2` is an irrational number.

Therefore 2a is irrational or a is irrational

Therefore `1/sqrt2` is irrational. Hence proved

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2014 to Current)
Chapter 1: Real Numbers
Ex.1.3 | Q: 3.1 | Page no. 14
Solution Prove that the Following is Irrational 1 √ 2 Concept: Revisiting Irrational Numbers.
S
View in app×