Question

show that 3√2 is irrational​

Answer 1

Answer:

We have to prove that 3✓2 is irrational.

Let us assume the opposite,

i.e.. 3✓2 is rational.

Hence,

3✓2 can be written in the form a/b.

where a and b (b≠0) are co-prime (no common factor other than 1)

Hence,

»» 3✓2 = a/b

»» ✓2 = 1/3 × a/b

»» ✓2 = a/3b

Here, a/3b is a rational number.

But, ✓2 is irrational number.

Since, Rational≠irrational

Hence, 3✓2 is irrational.

Hence proved.

Answer 2

Step-by-step explanation:

Solution :

Consider, 3√2 is rational

3√2 = a/b (a and b are integers and co - prime numbers)

3√2 × b = a

3√2b = a

Squaring both sides

36b² = a² ---------- (i)

If a² = 36b², 36 is a factor of a.

a = 36c ---------- (ii)

Put (ii) in (i),

36b² = (36c)²

36b² = 1296c²

b² = 36c²

If b² = 36c², 36 is a factor of b too.

a and b are coprime numbers but both have 36 as common factor. This is a contradiction to the assumption, this contradiction was arisen due to the wrong assumption.

Therefore, 3√2 is irrational.