Question

(ii) Show that 3+ V
$3 + \sqrt{5}$
5 is irrationai.​

Answer 1

Required Answer:-

Question:

• Prove that 3 + √5 is irrational.

Proof:

Let us assume that 3 + √5 is a rational number, say r.

Then,

3 + √5 = r

➡ √5 = r - 3

As r is rational, r - 3 is rational

➡ √5 is rational.

But this contradicts the fact that √5 is irrational.

Hence, our assumption is wrong.

Therefore,

3 + √5 is irrational. (Hence Proved)

Learn More:

1. Rational Number: A number that can be represented in p/q form where p and q are integers, q ≠ 0 and p, q have no common factors (except 1).
2. Examples: 3, 5/6, 1/99, 252, etc.
3. Irrational Number: A number that cannot be represented in p/q form where p and q are integers, q ≠ 0 and p, q have no common factors(except 1).
4. Examples: √3, √5, √12 etc.

Answer 2

Answer:

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