CBSE Class 10 Answered
show that root 3 is an irrational number
Asked by ajayrath7 | 12 Mar, 2019, 11:52: AM
Expert Answer
Let us start with the contrary, √3 is a rational number.
Hence √3 = a/b ..................(1)
where a and b are prime integers and no comman factor between a and b.
hence √3b = a
By squaring both sides, 3b2 = a2 or a2 / 3 = b2 ..............(2)
eqn.(2) shows 3 is a factor of a2 . If a is a prime number, then 3 also should be factor of a.
If 3 is a factor of a, then this contradicts the assumption we made for eqn.(1), that a is a prime number.
Hence √3 is not a rational number , it is an irrational number
Answered by Thiyagarajan K | 12 Mar, 2019, 02:52: PM
Application Videos
Concept Videos
CBSE 10 - Maths
Asked by aditikaldate7 | 21 Apr, 2024, 03:16: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by pathaksuman622 | 21 Apr, 2024, 11:56: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by yalagondanikhil | 16 Apr, 2024, 12:25: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by rrajansinghakb199 | 08 Apr, 2024, 05:12: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by nagalaxmidurgarao937 | 08 Apr, 2024, 01:42: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by mraniruddha03 | 02 Apr, 2024, 06:44: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by muttenenimalleswarrao | 29 Mar, 2024, 08:32: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by pathakvaishnavi9139 | 23 Mar, 2024, 10:45: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by mustafahssn786 | 23 Mar, 2024, 06:25: AM
ANSWERED BY EXPERT