Question

Which of the condition imply that the real no x is rational 1)x^1/2 is rational 2)x^2 and x^5 is a rational 3) x^2 and x^4 is arational

Answer 1

x² and x^4 is rational is the condition imply that the real no x is rational

Answer 2

Both 1 and 2

Take x =√2

x^½=√2^½=2^¼

2^¼ is irrational.

Take x=2

x^½=2^½=¼

¼ is rational.

So it can tell us if x is rational or not.

Similarly,

Take x=√2

x^5=(√2)^5=2^5/2

2^5/2 is irrational.

Take x=2

x^5=2^5=32

32 is rational.

So it can tell us if x is rational or not.

But, x^2 and x^4 cannot.

So, the answer is both (1) and (2).