Question

14.Prove that 7-5 under root 7 is an irrational number.​

Answer 1

Answer:

7√5 = p/q. As, we can see that p/7q is rational so √5 should also be rational. But this contradict the fact that √5 is irrational. So, by this we can say that 7√5 is irrational number

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Answer 2

Let us assume that 7√5 is rational number

Hence, 7√5 can be written in the form of a/b where a, b are co-prime and b not equal to 0.

7√5 = a/b

√5 = a/7b

here √5 is irrational and a/7b is rational number.

Rational number ≠ Irrational number

It is contradiction to our assumption 7√5 is rational number.

Therefore, 7√5 is an irrational number.

Hence, proved.