Identify the variable expression for the relationship below: the sum of 5 and the square of a number.
A. [tex]$5^2 n$[/tex]
B. [tex]$(5 n)^2$[/tex]
C. [tex]$5+n^2$[/tex]
D. [tex]$(5+n)^2$[/tex]
Answer (2)
Represent the unknown number with the variable n .
Express the square of the number as n 2 .
Add 5 to the square of the number: 5 + n 2 .
The variable expression is 5 + n 2 .
Explanation
Understanding the Phrase Let's break down the given phrase: 'the sum of 5 and the square of a number'. We need to translate this into an algebraic expression.
Representing the Number First, we represent the unknown 'number' with a variable. Let's use 'n'.
Squaring the Number Next, we need to express 'the square of a number'. This means we take our variable 'n' and raise it to the power of 2, which is written as n 2 .
Adding 5 to the Square Finally, we need to express 'the sum of 5 and the square of a number'. This means we add 5 to n 2 . So, the expression becomes 5 + n 2 .
Examples
Imagine you're designing a square garden and want to add a 5-foot wide path around it. If 'n' represents the side length of the garden, then the total area of the garden and the path can be represented by an expression involving the square of a number and a constant. This kind of algebraic thinking helps in many real-world design and planning problems.
The variable expression for 'the sum of 5 and the square of a number' is 5 + n 2 . Therefore, the correct answer is C. 5 + n 2 .
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