Question

Show that 3√7 is an irrational number. ​

Answer 1

Step-by-step explanation:

LET US TAKE ON CONTRARY THAT 3√7 IS RATIONAL. WHEREAS RHS IS RATIONAL. THIS CONTRADICTION HAS ARISED DUE TO OUR WRONG ASSUMPTION IN BEGINNING. THEREFORE 3√7 IS AN IRRATIONAL NUMBER

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Answer 2

Answer:

Let us assume to the contrary that 3√7 is a rational number

Then , 3√7 = a÷b where a and b are coprime integers and b not equal to 0

√7 = a÷3b

Therefore , we get a÷3b as rational

So √7 is also rational.

But this contradicts the fact that √7 is irrational

This contradiction has arisen because of our incorrect assumption that 3√7 is rational.

So we conclude that 3√7 is irrational.

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