Question

prove that 3√3 is irrational​

Answer 1

Explanation:

Let us assume that 3−

3

is a rational number

Then. there exist coprime integers p, q,q



=0 such that

3−

3

=

q

p

=>

3

=3−

q

p

Here, 3−

q

p

is a rational number, but

3

is an irrational number.

But, an irrational cannot be equal to a rational number.This is a contradiction.

Thus, our assumption is wrong.

Therefore 3−

3

is an irrational number.

Answer 2

AnsWer:-

✪Let us assume 3√3 to be Rational.

๛i.e 3√3=$\frac{a}{b}$

[•°•where a & b are co-prime integers and a&b≠0]

↝3√3=$\frac{a}{b}$

↝√3=$\frac{a}{b \times 3}$

↝√3=$\frac{a}{3b}$

✪√3=irrational

✪$\frac{a}{3b}$= Rational

★This creates a Contradiction and Proves that 3√3 is Irrational★

♦Also, Our Assumption is Wrong, LHS≠RHS♦

➜3√3 is Irrational

$\rule{200}{2}$