Is 125 a perfect square?
A. No, because there is no whole number that when multiplied by itself gives 125.
B. No, because perfect squares must be even numbers.
C. Yes, because 555 125, so 125 is a perfect square.
D. Yes, because 125 = 100+25, and 100 and 25 are both perfect squares, so 125 will also be a perfect square.
The Correct Answer and Explanation is:
The correct answer is A. No, because there is no whole number that when multiplied by itself gives 125.
A perfect square is a number that can be expressed as the product of a whole number multiplied by itself. In other words, a number ( x ) is a perfect square if there exists an integer ( n ) such that ( n \times n = x ) or ( n^2 = x ).
To determine whether 125 is a perfect square, we need to find out if there is a whole number that, when squared, equals 125.
Let’s check:
- ( 11 \times 11 = 121 )
- ( 12 \times 12 = 144 )
Since 125 falls between these two squares (121 and 144), there is no whole number whose square is exactly 125. Therefore, 125 is not a perfect square.
Why Answer B, C, and D Are Incorrect:
- Answer B states that “perfect squares must be even numbers.” This is incorrect because perfect squares can be either even or odd. For example, 9 is a perfect square (since ( 3 \times 3 = 9 )), and 9 is odd.
- Answer C seems to suggest that because 555 equals 125 (which is not true), 125 must be a perfect square. This reasoning is flawed, as it is based on a nonsensical equation and doesn’t follow the correct definition of a perfect square.
- Answer D argues that since 125 is the sum of 100 and 25, both of which are perfect squares, 125 should also be a perfect square. However, the sum of two perfect squares does not necessarily result in a perfect square. For instance, while 100 and 25 are indeed perfect squares, their sum (125) is not.
In conclusion, 125 is not a perfect square because there is no integer that, when multiplied by itself, results in 125.