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Rama09 [41]
3 years ago
11

In a 4-digit perfect square, the first two digits are the same, and the last two digits are also the same. What is the value of

this 4-digit number?
Mathematics
1 answer:
Firlakuza [10]3 years ago
6 0

Answer:

  • 7744

Step-by-step explanation:

Let the number is in the form of aabb.

<u>We can put it as:</u>

  • aabb = 11*(100a + b) = 11*(99a + a + b)

The number is a perfect square so it must be divisible by 11.

It is divisible by 11 if (a + b) is divisible by 11..

On the other hand, b = 0, 1, 4, 5, 6, 9 as the last digit of a perfect square.

Also, both a and b must be within (0,9) interval.

<u>Considering the above conditions we have options:</u>

  • a,b = 2,9 or 5,6 or 6,5 or 7,4

<u>The numbers are:</u>

  • 2299
  • 5566
  • 6655
  • 7744

<u>By testing we confirm only one of them is a perfect square: </u>

  • 7744
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