Question

Prove that 3√5-7 is irrational

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 √5 irrational
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Here is the process:

Let √5 is rational no. a/b where a and b are coprime

cross multiplying √5 and a/b

a = √5b

Squaring both sides

a² = 5b² ⇒ Equation 1

a²/5 = b²

⇒5 divide a²
⇒5 divide a

Putting a = 5c in equation 1

(5c)² = 5b²

25c² = 5b²

5c² = b²

c² = b²/5

⇒5 divide b²
⇒5 divide b



5 divide both a and b and our assumption was wrong.
So we conclude that √5 is irrational and hence 3√5 - 7 is irrational

Hence Proved.

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