Question

prove that 3root 5-3root 3 is an irrational number ​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let 3√5-5√3 be rational

Then

3√5-5√3=p/q

(3√5-5√3)²=p²/q²

(3√5)²+(5√3)²-2(3√5)(5√3)=p²/q²

45+75-30√15=p²/q²

120-30√15=p²/q²

30(4-√15)=p²/q²

4-√15=p²/30q²

√15=4-p²/30q²

For some p, q,, p²/30q² is rational and 4 is also rational.

So, 4-p²/30q² is rational

But √15 is irrational

3√5-5√3=Rational doesn't satisfy the condition

So 3√5-5√3 is irrational