Question

prove that 7–2√2 is irrational number.

Answer 1

Heya here is your answer:
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If we add, multiply, divide, subtract anything from any irrational number then the whole no. becomes irrational so we just have to prove √2 irrational
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Here is the process:

Let √2 is rational no. a/b where a and b are co-prime

cross multiplying √2 and a/b

a = √2b

Squaring both sides

a² = 2b² ⇒ Equation 1

a²/2 = b²

⇒2 divide a²
⇒2 divide a

Putting a = 2c in equation 1

(2c)² = 2b²

4c² = 2b²

2c² = b²

c² = b²/2

⇒2 divide b²
⇒2 divide b



2 divide both a and b and our assumption was wrong.
So we conclude that √5 is irrational and hence 7-2√2  is irrational

Hence Proved.

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