Which of the following will be an integer under the square

Question

Which of the following will be an integer under the square root? a. 159076 b. 946729 c. 14980 d. 78098 e. 11111 No answer only please on this one!

Fig · Answer

(B) for me

Why? In a^2 = a*a = c, the unit digit of c must be the square of an integer. Thus, (a) & (b) are out. What about 0 as a unit?.... If the unit digit is 0, the tenth must be 0, because we could be able to factorise : 10 * 10 from a^2. So, (c) is out Finally, 11111 is obviously not a square of an integer. (B)

seofah · Answer

The unit digit of c does not have to be the square of an integer. In fact: x1*x1=x1 x2*x2=x4 x3*x3=x9 x4*x4=x6 x5*x5*=x25 x6*x6=x6 x7*x7=x9 x8*x8=x4 x9*x9=x1 x10*x10=x00 where x is digits preceding the last digit. I told you not to use calculator :lol:

Fig · Answer

x is not correct too

For instance, 11 * 11 = 121

Summer3 · Answer

Fig, what if 6^2 = 36, the unit digit of 36 is 6 and it is not a square of any integer....OR 14^2 = 196 same case here...
Please explain.

seofah · Answer

Sorry, x is there just to denote preceding digits. It doesn't follow strict rules.

E.g. x9*x9=x1 is eqvt to ,say, 1 9 *1 9 =36 1

Fig · Answer

I went too fast

... It's not the way to solve

.... I got the luck this time to fall on the right one because using a wrong reasonning

Caas · Answer

Hi, First I narrowed down to A and B answer choices, taking into considaration unit digits. ...6^2=...6, ....4^2=....6 (for A) and .....3^2=.....9 (for B). Then we have to choose between A and B without calculator. I took (A) first. 400^2=160 000. It is a bit more than 159076. Then square root of 159076 must be around 400, i.e. 39X. Unit digit is 6. So it can be either 396 or 394. Let's take 396^2, because it is bigger and hence closer to 400. We need to start calculating it manually to understand that the result will end with 16, not 76. So the answer is (B). :!:

qxjmba · Answer

B 

a and d are divisible by 2 but not by 4
c is divisible by 10 but not by 100

2 and 10 are not perfect squares. so rule out a,d and c.

12100 = 110^2
105^2 = 10000+1000+25 = 11025
106^2 = 10000 + 1200 + 36 = 12036

So, 11111 is not a square. 

That leaves B

Which of the following will be an integer under the square

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