Bunuel wrote:
Which of the following is a perfect square?
A. 649
B. 961
C. 1664
D. 2509
E. 100000
Solution.
Two important things before solving the problem to make easy.
-->
First, look at the units digit in every option, For example. 1) 64
9--> you can get 9 as a unit digit by squaring the digit 3 or 7.
2) 96
1---> you can get 1 as a unit digit by squaring the digit 1 or 9.
-->
Second, we know squares of 10,20,30,40,50 ,60... and Formula \((a+b)^2=a^2+2ab+b^2\)
Now for
Option A).649--> We know (20)^2=400, and (30)^2=900. So the digit should be between 20 and 30. try (20+
3)^2 or (20+
7)^2.
\((20+3)^2=400+120+9=529--No\)
\((20+7)^2=400+280+49=729--No\)
Option B).961--> we know that (30)^2=900, \((30+1)^2=900+60+1=961--->YES\)
try all remaining--\((30+9)^2=900+540+81=1521--->NO\)
Option C).1664--> we know that (40)^2=1600, \((40+2)^2=1600+160+4=1764-->NO\)
\((40+8)^2=1600+640+64=2304---> NO.\)
Option D) 2509-->. We know that (50)^2=2500, \((50+3)^2=2500+300+9=2809--> NO\)
\((50+7)^2=2500+700+49=3249--> NO\)
E) No need to check as it has odd number of 0'-->no.
Ans.B