Answer:
Step-by-step explanation:
- Let us assume, the contrary √3 is a rational no.
- √3 = p/q ,where p and q are co-prime
- p = √3q
- squaring on both sides
- [tex]p^{2}[/tex]/3 =[tex]q^{2}[/tex].............................(1)
- 3 is a factor of p
- p = 3c , where c is some constant
- substituting p = 3c in equation (1)
- 9[tex]c^{2}[/tex] = 3[tex]q^{2}[/tex]
- [tex]q^{2}[/tex]/3 = [tex]c^{2}[/tex]
∴ 3 is also a factor of q
- But , this is a contradiction.
- we have assume p and q are co prime
∴ √3 is an irrational no.
