Prove that root 2 is an irrational number

Asked by admin @ 24/08/2021 in Math viewed by 267 People

Proof that root 2 is irrational

Answered by admin @ 24/08/2021

Let √2 be a rational number

Therefore, √2= p/q [ p and q are in their least terms i.e., HCF of (p,q)=1 and q ≠ 0

On squaring both sides, we get
p²= 2q² ...(1)
Clearly, 2 is a factor of 2q²
⇒ 2 is a factor of p² [since, 2q²=p²]
⇒ 2 is a factor of p

Let p =2 m for all m ( where m is a positive integer)

Squaring both sides, we get
p²= 4 m² ...(2)
From (1) and (2), we get
2q² = 4m² ⇒ q²= 2m²
Clearly, 2 is a factor of 2m²
⇒ 2 is a factor of q² [since, q² = 2m²]
⇒ 2 is a factor of q

Thus, we see that both p and q have common factor 2 which is a contradiction that H.C.F. of (p,q)= 1

Therefore, Our supposition is wrong

Hence √2 is not a rational number i.e., irrational number.

Prove that root 2 is an irrational number

Similar Questions

Prove that root 2 root 3 is irrational number

Prove that 2 root 5 is an irrational number

Prove that 2 root 3 is an irrational number

Prove that 3 2 root 5 is irrational number

Prove that 1 by root 2 is irrational

Prove that root 7 is an irrational number

Prove that root 5 is an irrational number

Prove that root 3 is an irrational number

Prove that 5 root 3 is an irrational number

Prove that 7 root 5 is an irrational number

Prove that root 3 root 5 is irrational number

Prove that under root 5 is an irrational number

Prove that 3 root 5 is an irrational number

Prove that under root 3 is an irrational number

Prove that square root of 7 is an irrational number

Most viewed questions in Math

What is the value of x in the expression

Shubham is facing south and moves 30 km

Prachi excellence in mathematics class 7 solutions pdf free download

Oxford new enjoying mathematics class 7 solutions chapter 1

Survey of various types of bank accounts icse project

The town of p is located at point x

A clock gains 4 minutes after every 4 minutes

Running a tuck shop or canteen maths project pdf

Paul is sixteenth from the front of the row

The average weight of 20 teachers is 80 kg

The number 567 xy is completely divisible by 30

In a row of friends tiya occupies fifteenth place

What would $ mean if fat is coded as

Consider a 3 digit integer x with distinct digits

Rahul went to his mother's mother in law