Question

prove tha √2 is an irrational numbers.​

Answer 1

Answer:

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Explanation:

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Answer 2

To Prove:

√2 is an irrational number.

Proof:

To prove √2 is an irrational number.

Let us assume √2 as a rational number.

We known that,

Rational numbers are written in the form of p/q.

=> √2 = p/q

Squaring on both sides.

=> 2 = (p/q)²

=> 2q² = p —— ⓵

=> p²/2 = q²

Hence, 2 divides p and p is a multiple of 2.

=> p = 2m

=> p² = 4m² —— ⓶

From ⓵ & ⓶,

=> 2q² = 4m²

=> q² = 2m²

• q² is a multiple of 2.
• q is a multiple of 2.

Hence, p and q have common factor 2.

Therefore, Our assumption is wrong that √2 is a rational number.

∴ √2 is an irrational number.

Hence Proved.