A-four-digit-number-has-the-following-properties-a-It-is-a-perfect-square-b-The-first-two-digits-are-equal-c-The-last-two-digits-are-equal-Find-all-such-numbers-

Question Number 13391 by Tinkutara last updated on 19/May/17

A four digit number has the following

properties :

(a) It is a perfect square

(b) The first two digits are equal

(c) The last two digits are equal .

Find all such numbers .

Answered by RasheedSindhi last updated on 19/May/17

let the number is

x + 10 x + 100 y + 1000 y

= 11 x + 1100 y

= 11 (x + 100 y)

Since the number is perfect

square it contains every prime

factor twice . So

11 \times 11 = 121 is the divisor of

the required number .

Let the number is {121 m}^{2}

Since the number is of four

digits {121 m}^{2} ⩽ 9999

11 m < 99

Hence the square root of the

number may be

11, 22, 33, \dots, 99

On testing each of these

numbers only 88 is such number

whose square fulfills the

requirements

88^{2} = 7744

Commented by RasheedSindhi last updated on 19/May/17

{It}^{'} s complete now .

Commented by mrW1 last updated on 20/May/17

G r e a t!

Commented by RasheedSindhi last updated on 20/May/17

\overset{↢}{! 1 Wrm tol a sknahT}