Question

Prove that root 3 is essational​

Answer 1

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Proof:- [Contradiction Method]

Let us Assume that √3 is rational Number.

√3 = p/q where p&q are Integers and q≠0

Also, p&q are co-prime.

By Squaring on Both Sides,

(√3)² = [p/q]²

3 = p²/q²

3q² = p²_____(1)

=> p² is divisible by 3

=> p is also divisible by 3

p = 3r where r is any integer.

By Squaring on both sides,

p² = [3r]²

p² = 9r²______(2)

From (1),

3q² = 9r² [Cancelin 3 Tables]

q² = 3r²√√√√√

=> p² is divisible by 3

=> p is also divisible by 3

Therefore, '3' is Common Factor for both p&q

This Contradicts that p&q are co-prime.

So, Our Assumption √3 is Rational is wrong ❌

Therefore, √3 is an irrational Number.

• I Hope it's Helpful My Friend.

Answer 2

Step-by-step explanation:

Proof:- [Contradiction Method]

Let us Assume that √3 is rational Number.

√3 = p/q where p&q are Integers and q≠0

Also, p&q are co-prime.

By Squaring on Both Sides,

(√3)² = [p/q]²

3 = p²/q²

3q² = p²_____(1)

ANSWER

=> p² is divisible by 3