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Which of the following numbers is a perfect square?
222
196
124
141
196
Check the last digits: perfect squares cannot end in 2, 3, 7, or 8. Numbers 222, 124, and 141 violate this, leaving only 196.
A set of four numbers: 222, 196, 124, 141.
n2=P
Check the last digits: perfect squares cannot end in 2, 3, 7, or 8. Numbers 222, 124, and 141 violate this, leaving only 196.
Many students mistake numbers ending in 4 or 6 as always being perfect squares without verifying the actual root, but here the elimination method is sufficient.
Analyze the ending digits
A perfect square of an integer can only end in the digits 0, 1, 4, 5, 6, or 9. Let's check our options.
endingтИИ{0,1,4,5,6,9}
Evaluate Option A
The number 222 ends in 2, which is not a possible unit digit for a perfect square.
222юАа=n2
Evaluate Option B
The number 196 ends in 6. We know that 142=196.
142=196
Evaluate Options C and D
The number 124 ends in 4, but is not a perfect square (it is 4├Ч31). The number 141 ends in 1, but its root is approximately 11.87.
124юАа=n2,141юАа=n2
B is correct because 196 is the square of the integer 14, while the other provided numbers are not perfect squares.
Understanding unit digit patterns is crucial for quick mental math in competitive exams for both identifying squares and calculating square roots.
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