prove that
[tex]1 \div \sqrt{2 } [/tex]
is irrational...
Share
prove that
[tex]1 \div \sqrt{2 } [/tex]
is irrational...
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Let us assume that √2 is irrational
1/√2 = p/q (where p and q are co prime)
q/p = √2
q = √2p
squaring both sides
q² = 2p² .....................(1)
By theorem
q is divisible by 2
∴ q = 2c ( where c is an integer)
putting the value of q in equitation 1
2p² = q² = 2c² =4c²
p² =4c² /2 = 2c²
p²/2 = c²
by theorem p is also divisible by 2
But p and q are coprime
This is a contradiction which has arisen due to our wrong assumption
∴1/√2 is irrational
♥️ HEYA ♥️
here is your answer
HOPEFULLY THIS HELPS
MARK AS BRAINLIEST
#KHUSHI✌️