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Find all six digited natural numbers abcd66 which are perfect squares.

Find all six digited natural numbers abcd66 which are perfect
squares.

Grade:10

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago

Hello student,
Please find the answer to your question below
Number format is :abcd66 . Now it should be between 100066 to 999966 .
So number should lie between 316 and 999 . (app root of above number .)
Now we can write this as (a*100 + b)2 ,where b is less than 100.
Now it will totally depend on b .
We know that from 1 to 100 , square of no number ends with 66 .
because unit digit is 6 means that number should end with 4 or 6 .
square of numbers ending with 4 or 6 last 2 digit will 16 ,36,56,76 or 96 .
So there is no number which is satisfying this criteria .
Hope this would have cleared your doubt .

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