Question

prove that the following are irrational (1)1/√2 (2)7√5

Answer 1

Lucent book is very good for 11th maths if you want not a book then download lucent app. (www.lucent publication. App. In).

Answer 2

1. To prove that 1/√2 is irrational.

Using Contradiction Method:

Proof: Let us consider that 1/√2 is rational.

Thus, 1/√2 = p/q [Where p and q are integers and q ≠ 0]

⇒ 1/√2 = p²/q²

⇒ 2p² = q²

⇒ q = p√2, which is false as √2 is irrational, so q cannot be rational.

Hence, it leads to contradiction of the fact that 1/√2 is rational.
Thus, 1/√2 is irrational.

2. Similarly for 1/√5 do the same as above.