Problem 5:
We say that a number has a 'square root' if we find another integer which gives us the first number if multiplied by itself. For example, $4$ has a square root since , but $5$ has no square root. Out of the $100$ numbers from $1$ to $100$, how many integers have square roots?
BdMO National Primary 2011/5 (Junior 2011/1)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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Re: BdMO National Primary 2011/5 (Junior 2011/1)
@ataher.sams
please, post the way of getting the answer along with it.
here, we just have to find the largest number smaller or equal to $100$.which is $100$ so the answer will be $\sqrt {100}=10$
please, post the way of getting the answer along with it.
here, we just have to find the largest number smaller or equal to $100$.which is $100$ so the answer will be $\sqrt {100}=10$
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: BdMO National Primary 2011/5 (Junior 2011/1)
\[\sqrt{100}=10\]
Then the numbers are .....\[1^{2},2^{2},3^{2},4^{2},5^{2},6^{2},7^{2},8^{2},9^{2} And 10^{2}\]
Then the numbers are .....\[1^{2},2^{2},3^{2},4^{2},5^{2},6^{2},7^{2},8^{2},9^{2} And 10^{2}\]
Re: BdMO National Primary 2011/5 (Junior 2011/1)
answer is 10