show that 2 minus root 3 is irrational
Answers
Answered by
1
Hi there !
To prove:-
2 - √3 is irrational
Lets assume that 2 - √3 is rational.
Let ,
2 - √3 = r , where r is a rational number
Squaring both the sides ,
[2 - √3 ]² = r²
4 - 4√3 + 3 = r²
7 - 4√3 = r²
- 4√3 = r² - 7
√3 = r² - 7 / -4
Here ,
RHS is purely rational. But , LHS [√3 ] is irrational.
This is a contradiction.
Hence , our assumption is wrong.
Therefore , 2 - √3 is irrational
To prove:-
2 - √3 is irrational
Lets assume that 2 - √3 is rational.
Let ,
2 - √3 = r , where r is a rational number
Squaring both the sides ,
[2 - √3 ]² = r²
4 - 4√3 + 3 = r²
7 - 4√3 = r²
- 4√3 = r² - 7
√3 = r² - 7 / -4
Here ,
RHS is purely rational. But , LHS [√3 ] is irrational.
This is a contradiction.
Hence , our assumption is wrong.
Therefore , 2 - √3 is irrational
Similar questions