Prove that `2sqrt3` is an irrational number – InterviewSolution

InterviewSolution

1.	Prove that `2sqrt3` is an irrational number
Answer» Rational numbers can be written in the form `p/q` where `p` and `q` are intergers and `q !=0`. Now, given number is , `2sqrt3 = 2sqrt3**sqrt3/sqrt3 = 6/sqrt3` So, it is in `p/q` form and `q !=0`. But, as `q` is not an integer, given number is not a rational number. Hence, `2sqrt3` is an irrational number.

Discussion

No Comment Found

Related InterviewSolutions

Decide whether the number `0.120120012000012….` Is rational or not. Give reason to support your answer.
Show that each of the following numbers is rational. What can you say about the prime factors of their denominators ? (i) 23.123456789 (ii) 32. `overline(123456789)`
In a school there are two sections, namely A and B, of class X. there are `30` students in section A and `28` students in section B. find the minimum number of books required for their class library so that they can be distributed equally among students of section A ore section B.
The mode of the following frequency distribution is 46 and the total frequency is 150. Find the missing frequencies x and y.
Prove that `sqrt(11)` is irrational.
Prove that `sqrt(5)` is irrational.
In the given figure, ABCD is a cyclic quadrilateral; O is the centre of the circle.If `/_BOD=160^@`, then find `/_BPD`.
The product of two consecutive integers is divisible by 2. Is this statement true or false. Give Reason?
A girl is twice as old as her sister. four years hence , the product of their ages (in years) will be 160 . Find their present ages?
Prove that one of every three consecutive positive integers isdivisible by 3.