How many integers between 200 and 300 are perfect squares?
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How many integers between 200 and 300 are perfect squares?
We know 10 x 10 = 100.
Working from there:
11 x 11 = 121
12 x 12 = 144
13x 13 = 169
14 x 14 = 196
15x15 = 225 but that's over 200.
So there are four perfect squares between 100 and 200 (not inclusive of 100)
Essentially, the same idea as Gusbob:Quote:
Originally Posted by sri340
How many integers between those two numbers?
You can also use a progression.
Say, (note difference
).
How many terms betweenand
? :)
Start from the biggest square under. Now many
with
can you fit in
?
Is there any sum of terms ofwith
consecutive that fit into
? Sure ! We have
, but we cannot fit
, so there are only three perfect squares between
There ... must be a better way to explain this, though ..
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I know this solution is a bit useless and boring after the previous answers, but eh, this is worth a post :D