Question

Provethatroot2-3root5isirrational

Answer 1

Answer:

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Let √2-3√5 is a rational number.

As we know, a rational number can be written in the form of p/q where p,q are integers.

√2-3√5=p/q

(√2-3√5)²=(p/q)²

√2²+(3√5)²-2(√2)(3√5)=p²/q²

(2+45-6√10)=p²/q²

6√10=p²/q²-47

√10=(p²-47q²)6q²

Hence, (p²-47q²)/6q² is a rational number.

But √10 is an irrational number.

Hence,√2-3√5 is irrational number.

(Proved)

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