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555-605 (Medium)|   Algebra|      
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Bunuel
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The smallest number added to 680621 to make the sum a perfect square 10 May 2022, 08:15
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25% (medium)

Question Stats:

76% (01:42) correct 24% (01:25) wrong based on 161 sessions

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The smallest number added to 680621 to make the sum a perfect square is:

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
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A
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The smallest number added to 680621 to make the sum a perfect square 10 May 2022, 08:23
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Bunuel
The smallest number added to 680621 to make the sum a perfect square is:

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
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Must be (A) , as \(680621 + 4 = 680625\)

Again, \(\sqrt{680625}=825\)
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BadukMagician
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The smallest number added to 680621 to make the sum a perfect square 12 Sep 2025, 12:01
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This is probably the wrong way to think about it, but I saw 621, and knew 625 is a perf square so I just said A

Bunuel
The smallest number added to 680621 to make the sum a perfect square is:

(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
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okHedwig
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The smallest number added to 680621 to make the sum a perfect square 12 Sep 2025, 23:28
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Hi,
I solved this question but took me a long time to solve it, how to solve it efficiently?
Please guide. Thank you
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paragw
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The smallest number added to 680621 to make the sum a perfect square 29 Sep 2025, 01:32
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Let x should be added to the number so that it becomes a Perfect Square (PS)
Any PS gives us the unit digit as 1, 4, 5, 6, 9
x can only be 0, 3, 4, 5, 8
See the options, we only have 4, 5 , 8
Eliminate options C & E
Now we know that 800^2 = 640000
Therefore our resultant number should be greater than 800
Now we'll proceed with x=4 coz after adding 4, we'll get 680625, which is divisible by 625 (a PS)
680625 = 1089*625 = (33*25)^2
Hence, x=4
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