Question

Show that 8^1/2 is not an integer

Answer 1

Answer on Question #82410 – Math – Real Analysis

Question

Show that $8^{1/2}$ is not an integer.

Solution

The set of integers, denoted by $\mathbb{Z}$, is formally defined as follows:

$$Z = \{ \dots, -3, -2, -1, 0, 1, 2, 3, \dots \}$$

Integers include natural numbers (counting numbers), the opposites of the natural numbers and zero.

$4^{1/2} = 2,2 > 0$, since $2^2 = 4$

$9^{1/2} = 3,3 > 0$, since $3^2 = 9$

$0 < 4 < 8 < 9 \Rightarrow 4^{1/2} < 8^{1/2} < 9^{1/2}$

Then $2 < 8^{1/2} < 3$

There is no integer number between 2 and 3.

Thus, $8^{1/2}$ is not an integer.

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