Question

Prove that 5 + 2√5 is an irrational number

Answer 1

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Given:-

Prove that 5 + 2√5 is an irrational number

Solution:-

Let us assume that 5 + 2√5 is a rational number.

So, it can be written in the form a/b

5 + 2√5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving 5 + 2√5 = a/b we get,

=>2√5 = a/b – 5

=>2√5 = (a-5b)/b

=>√5 = (a-5b)/2b

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

So, it contradicts our assumption. Our assumption of 5 + 2√5 is a rational number is incorrect.

5+ 2√5 is an irrational number

Step-by-step explanation:

Hope it helps you

Answer 2

Answer:

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