Question

the value of n for which √n be a rational number

Answer 1

it can be 4,9,16,25,... all perfect squares

Answer 2

Answer:

The value of n for which root n exists a rational number is 4.

Step-by-step explanation:

Let n be a natural number.

Case I:

n is a perfect square $(1,4,9,16,25, \ldots .)$

Then $\sqrt{\mathrm{n}}$ exists a natural number.

$\sqrt{1}, \sqrt{4}, \sqrt{9}, \sqrt{16}, \sqrt{25}$, etc. are all natural numbers.

Case II:

n exists not a perfect square $(2,3,5,6,7,8, \ldots)$  

$\sqrt{2}, \sqrt{3}, \sqrt{5}, \sqrt{6}, \sqrt{7}$ etc. are all irrational.

$\sqrt{n}$ is either a natural number of an irrational number.

The value of n for which root n exists a rational number is 4.

Therefore, the value of n for which $\sqrt{n}$ be a rational number is 4.

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