Question

If root 5 is an irrational number. Prove that 3 - root 5 is also an irrational number ​

Answer 1

Answer:

Let us assume that 3 + √5 is a rational number. Here, {(a - 3b) ÷ b} is a rational number. But we know that √5 is a irrational number. So, {(a - 3b) ÷ b} is also a irrational number.

Step-by-step explanation:

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Answer 2

To Prove :-

• 3 - √5 is an irrational number.

Proof :-

Let us assume to the contrary, that 3 - √5 is rational.

Then, there exist co-primes a and b (b ≠ 0) such that

⇒ 3 - √5 = a/b

⇒ √5 = 3 - a/b

Here

• 3 - a/b is a rational number and √5 is an irrational number.

But, a rational number can't equal to an irrational number.

This is contradiction.

Thus, our assumption is wrong.

Therefore, 3 - √5 is an irrational number.

Hence, Proved !