Question

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

With proper solutions ​

Answer 1

Answer:

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Answer 2

Answer:

Answer:

Given 3 + √5

To prove:3 + √5 is an irrational number.

Proof:

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

So it can be written in the form a/b

3 + √5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving

3 + √5 = a/b

we get,

=>√5 = a/b – 3

=>√5 = (a-3b)/b

=>√5 = (a-3b)/b

This shows (a-3b)/b is a rational number.

But we know that √5 is an irrational number, which contradicts our assumption.

Our assumption 3 + √5 is a rational number is incorrect.

3 + √5 is an irrational number

Hence proved.

Step-by-step explanation:

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