Which of the following pairs of numbers represents a perfect square and its square root?
A. 16 and [tex]$\sqrt{8}$[/tex]
B. 25 and [tex]$\sqrt{5}$[/tex]
C. 125 and 25
D. 256 and 16
Answer (2)
A perfect square and its square root are related such that the square root, when squared, equals the perfect square.
Check each option to see if the square of the second number equals the first number.
Option A: ( 8 ) 2 = 8 = 16 .
Option B: ( 5 ) 2 = 5 = 25 .
Option C: 2 5 2 = 625 = 125 .
Option D: 1 6 2 = 256 .
The correct pair is 256 and 16 .
Explanation
Problem Analysis We need to identify the pair of numbers where the first number is a perfect square and the second number is its square root. This means that if we square the second number, we should get the first number. Let's examine each option:
Checking Option A Option A: 16 and 8 . If we square 8 , we get 8, not 16. So, this is not the correct pair.
Checking Option B Option B: 25 and 5 . If we square 5 , we get 5, not 25. So, this is not the correct pair.
Checking Option C Option C: 125 and 25. If we square 25, we get 2 5 2 = 625 , not 125. So, this is not the correct pair.
Checking Option D Option D: 256 and 16. If we square 16, we get 1 6 2 = 256 . So, this is the correct pair.
Final Answer Therefore, the pair of numbers that represents a perfect square and its square root is 256 and 16.
Examples
Understanding perfect squares and square roots is crucial in various fields, such as engineering and architecture. For instance, when designing a square-shaped garden with an area of 256 square meters, knowing that the square root of 256 is 16 helps determine that each side of the garden should be 16 meters long. This concept is also fundamental in cryptography, where the difficulty of factoring large numbers into their prime factors (related to square roots) is used to secure data.
The correct pair of numbers that represents a perfect square and its square root is 256 and 16, as squaring 16 results in 256. The other options do not satisfy the required condition. Thus, option D is the answer.
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