Which of the following four digit numbers is a perfect square such that the first two digits and the last two digits considered separately
Which of the following four digit numbers is a perfect square such that the first two digits and the last two digits considered separately also represent perfect squares ?
(A) 1681
(B) 5462
(C) 8214
(D) 7210
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Correct option is (A) 1681
(A) 1681 = 1600+80+1 \(=40^2+2\times40\times1+1^2=(40+1)^2=41^2\)
\(\therefore\) 1681 is a perfect square.
Also, its first two digits \(=16=4^2\) is a perfect square.
And its last two digits \(=81=9^2\) is a perfect square.
Thus, 1681 is a type of required number.
(B) 5462 is not a perfect square because any number whose last digit (unit digit) is 2 never forms a perfect square.
Thus, 5462 is not a type of required number.
Similarly 8214 and 7210 are not a perfect square.
Thus, both are not a type of required number.
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