Question

Given that √5 is an irrational number. Hence prove that

3 +2√5 is also an irrational number.​

Answer 1

Answer:

Given:3 + 2√5

To prove:3 + 2√5 is an irrational number.

Proof:

Letus assume that 3 + 2√5 is a rational number.

Soit can be written in the form a/b

3 + 2√5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving3 + 2√5 = a/b we get,

=>2√5 = a/b – 3

=>2√5 = (a-3b)/b

=>√5 = (a-3b)/2b

This shows (a-3b)/2b is a rational number. But we know that But √5 is an irrational number.

so it contradictsour assumption.

Our assumption of3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number

Hence proved

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Answer 2

Step-by-step explanation:

To prove: 3 + 2√5 is an irrational number. Proof: Let us assume that 3 + 2√5 is a rational number. This shows (a-3b)/2b is a rational number.

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