Which statement explains why 49 is a perfect square?
A. 49 can be multiplied by 49.
B. 49 is equal to 7 plus 7.
C. 49 is between 36 and 64.
D. 49 is equal to 7 times 7.
Answer (1)
A perfect square is the square of an integer.
Check each statement to see if it aligns with the definition of a perfect square.
'49 is equal to 7 times 7' is the correct statement because 7 × 7 = 49 = 7 2 .
Therefore, 49 is a perfect square because it is the square of the integer 7, so the answer is: 49 is equal to 7 times 7 .
Explanation
Understanding Perfect Squares We need to determine which statement correctly explains why 49 is a perfect square. A perfect square is a number that can be obtained by squaring an integer. Let's examine each option.
Analyzing Statement 1 The first statement says '49 can be multiplied by 49'. While true, this describes 4 9 2 = 2401 , not why 49 itself is a perfect square.
Analyzing Statement 2 The second statement says '49 is equal to 7 plus 7'. This means 49 = 7 + 7 = 14 , which is false.
Analyzing Statement 3 The third statement says '49 is between 36 and 64'. While true, this doesn't explain why 49 is a perfect square. It only places 49 between two other perfect squares ( 6 2 = 36 and 8 2 = 64 ).
Analyzing Statement 4 The fourth statement says '49 is equal to 7 times 7'. This means 49 = 7 × 7 = 7 2 . This aligns perfectly with the definition of a perfect square, as it shows 49 is the result of squaring the integer 7.
Conclusion Therefore, the correct statement is '49 is equal to 7 times 7' because it demonstrates that 49 is the square of an integer (7).
Examples
Perfect squares are useful in many areas, such as calculating areas and volumes. For example, if you have a square garden with an area of 49 square feet, you know that each side of the garden is 7 feet long because 7 × 7 = 49 . Understanding perfect squares helps in simplifying calculations and visualizing spatial relationships.
