Question

Prove that 3+√5 is an irrational number.​

Answer 1

$\huge{●Answer ↴}$

Let 3 - √5 be a rational number

3 - √5 = p/q [ where p and q are integer , q ≠ 0 and q and p are co-prime number ]

=> √5 = 3 - p/q

=> √5 = (3q - p)/q

We know that number of form p/q is a rational number.

So, √5 is also a rational number.

But we know that √5 is irrational number. This contradicts our assumption.

Therefore, 3 - √5 is an irrational number.

❤"

Answer 2

Step-by-step explanation:

Prove that 3+√5 is an irrational number.

Prove that 3+√5 is an irrational number.Hint: To prove that 3+√5 is an irrational number, first assume it to be a rational number. ... As both p and q are integers, so p−3q is also an integer. As q is not equal to 0, p−3qq is a rational number. ⇒√5 = p−3qq is also a rational number.

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