$\sqrt{2016n}$. Solve for $n$

Question

What is the smallest natural number $n$ possible for $\sqrt{2016n}$ to be a whole integer?

I can solve it by using a calculator and with trial and error but I think I have to solve it without a calculator. How would you go about the question?

Thank you

It is $n=0$ (provided $0\in \Bbb{N}$, which is sometimes a convention). — Dietrich Burde, Oct 19 '18 at 08:30

score 9 · Answer 1 · answered Oct 19 '18 at 07:12

9

Guide:

$$2016 = 2^5\cdot 3^2 \cdot 7$$

This is not a square because the power of $2$ and $7$ are odd. What do you have to multiply to make them even?

answered Oct 19 '18 at 07:12

Siong Thye Goh

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$\sqrt{2016n}$. Solve for $n$

1 Answers1