Question

prove that 3 root7 is irrational​

Answer 1

let 3√7 be rational

then 3√7=a/b where a and b are integers

√7 =a/3b

since a and b are Integers therefore a/3b is rational but this contradicts the fact that √7 is irrational

hence 3√7 is irrational

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Answer 2

To prove : 3√7 is irrational number.

Proof : Let 3√7 not an irrational number.

i.e. let us assume 3√7 as rational number.

3√7 = p/q (p,q € Integers & q ≠ 0)

√7 = p/3q

But, p/3q is rational number and √7 is irrational number.

It is not possible.

Therefore, our assumption is wrong, i.e 3√7 is not an rational number, i.e 3√7 is an irrational number.