Question

Hey guys please answer​

Answer 1

Suppose 3√6 is a rational number,

Thus, by the property of rational number,

We can write,

Where, p and q are distinct  integers and q ≠ 0,

By squaring both sides,

------(1)

⇒ p² is a multiple of 54,

⇒ p is a multiple of 54

Thus, we can write,

p = 54a, where a is any number,

From equation (1),

⇒ q² is a multiple of 54,

⇒ q is a multiple of 54

Therefore, p and q are not distinct,

Which is a contradiction,

⇒ 3√6 is not a rational number,

Thus, 3√6 is an irrational number

Hence, proved......

Answer 2

Answer:

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