Which of the following is a perfect square?
A) 279
B) 115
C) 169
D) 154
Answer (2)
Check if the square root of each option is an integer.
Calculate 279 ≈ 16.70 which is not an integer.
Calculate 115 ≈ 10.72 which is not an integer.
Calculate 169 = 13 which is an integer, so 169 is a perfect square.
Calculate 154 ≈ 12.41 which is not an integer.
Explanation
Understanding Perfect Squares We are given four numbers and asked to identify which one is a perfect square. A perfect square is a number that can be obtained by squaring an integer. In other words, if the square root of a number is an integer, then the number is a perfect square.
Checking Each Option Let's examine each option:
Option A: 279. The square root of 279 is approximately 16.70. Since this is not an integer, 279 is not a perfect square.
Option B: 115. The square root of 115 is approximately 10.72. Since this is not an integer, 115 is not a perfect square.
Option C: 169. The square root of 169 is 13, since 13 × 13 = 169 . Since 13 is an integer, 169 is a perfect square.
Option D: 154. The square root of 154 is approximately 12.41. Since this is not an integer, 154 is not a perfect square.
Identifying the Perfect Square Therefore, the only perfect square among the given options is 169.
Final Answer The perfect square among the options is 169 .
Examples
Perfect squares are useful in various real-life situations. For example, when designing a square garden or room, knowing perfect squares helps determine the side lengths needed to achieve a specific area. If you want a square garden with an area of 169 square feet, you know that each side must be 13 feet long because 1 3 2 = 169 . This concept is also used in construction, architecture, and many other fields where precise measurements and square shapes are important.
The only perfect square among the options is 169, as its square root is 13, which is an integer. The other options do not yield an integer when their square roots are calculated. Thus, the answer is 169 .
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