Question

prove that it was irrational
I need full solution

Answer 1

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Answer 2

Hey!

2) 7√5

Let suppose 7√5 is rational number

7√5= P/q

√5=P/7q

Our contradiction is wrong because Rational can't be equal to irrational.

So 7√5 is irrational

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3. 6+√2

Let suppose 6+√2 be a rational number

P/q =6+√2

Squaring both sides

(P/q)²=(6+√2)²

Now use formula of (a+b)²=a²+2ab+b²

P²/q²=(6)²+2.6.√2+(√2)²

P²/q²=36+12√2+2

P²/q²=38+12√2

P²/q²-38= 12√2

Our contradiction is wrong because Rational can't be equal to irrational.

So 6+√2 is irrational

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Regards :)

Yash Raj ✌