How to prove that root p …
CBSE, JEE, NEET, CUET
Question Bank, Mock Tests, Exam Papers
NCERT Solutions, Sample Papers, Notes, Videos
Posted by Prem Bisht 6 years, 4 months ago
- 1 answers
Test
Related Questions
Posted by Kanika . 1 month ago
- 1 answers
Posted by Parinith Gowda Ms 3 months, 2 weeks ago
- 0 answers
Posted by Parinith Gowda Ms 3 months, 2 weeks ago
- 1 answers
Posted by Sahil Sahil 1 year, 4 months ago
- 2 answers
Posted by Vanshika Bhatnagar 1 year, 4 months ago
- 2 answers
Posted by Lakshay Kumar 1 year, 1 month ago
- 0 answers
Posted by Hari Anand 6 months, 1 week ago
- 0 answers
myCBSEguide
Trusted by 1 Crore+ Students
Test Generator
Create papers online. It's FREE.
CUET Mock Tests
75,000+ questions to practice only on myCBSEguide app
Sia ? 6 years, 4 months ago
Let us assume, to the contrary, that √p is rational.
So, we can find co-prime integers a and b(b ≠ 0)
{tex}\begin{array}{l}\sqrt p=\frac ab\\\end{array}{/tex}
{tex}a = b _ { \sqrt { P } }{/tex}
on squaring both sides we get
a2 = pb2 ...... (1)
so a2 is divisible by p
hence a is divisible by p ....... (2)
So, we can write a = pc for some integer c.
Squaring both the sides we get
a2 = p2 c2 ....
⇒ pb2 = p2 c2 ....[From (1)]
⇒ b2 = pc2
⇒ b2 is divisible by p
⇒ b is divisible by p ....... (3)
From (2) and (3) we conclude that p divides both a and b.
∴ a and b have at least p as a common factor.
But this contradicts the fact that a and b are co-prime. (As per our assumption)
This contradiction arises because we have assumed that √p is rational.
∴ √p is irrational.
0Thank You