Question

$prove \: that \: 3 + \sqrt[2]{5} \: is \: irrational.$
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Answer 1

Answer:

$\huge \sf {\orange {\underline {\pink{\underline {❥︎ Answer࿐}}}}}$

Given: 

3 + 2√5

To prove:

3 + 2√5 is an irrational number.

Proof:

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

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

3 + 2√5 = a/b

Here a and b are coprime numbers and b ≠ 0

Solving 3 + 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 √5 is an irrational number.

So, it contradicts our assumption. Our assumption of 3 + 2√5 is a rational number is incorrect.

3 + 2√5 is an irrational number

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Answer 2

Answer:

refer to the given attachment

Step-by-step explanation:

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