There are 200 perfect squares less than 1000 that have a ones digit of 2,3 or 4.
To check that perfect squares that have a ones digit of 2,3 or 4 :
First we will check the squares of 0-10 numbers.
[tex]0^{2} = 0[/tex] [tex]1^{2} = 1[/tex] [tex]2^{2} = 4[/tex]
[tex]3^{2} = 9[/tex] [tex]4^{2} = 16[/tex] [tex]5^{2} = 25[/tex]
[tex]6^{2}=36[/tex] [tex]7^{2}=49[/tex] [tex]8^{2}=64[/tex]
[tex]9^{2}=81[/tex] [tex]10^{2}=100[/tex]
As we can see, only 2,8 have the squares which have 2,3 or 4 at ones place.
So, only numbers like 12,18,24,28.........,998 have a ones digit of 2,3 or 4.
Hence, there are 200 perfect squares less than 1000 that have a ones digit of 2,3 or 4.
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