(Order of Operations with Radicals LC)
Simplify the expression.
square root of 36 minus 2 squared
2
10
16
32
The Correct Answer and Explanation is:
To simplify the expression (\sqrt{36} – 2^2), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Step 1: Calculate the square root
First, we simplify the square root:
[
\sqrt{36} = 6
]
This gives us the first part of the expression.
Step 2: Calculate the exponent
Next, we need to calculate (2^2):
[
2^2 = 4
]
Now we can rewrite the expression with the results from the previous calculations:
[
6 – 4
]
Step 3: Perform the subtraction
Now, we perform the subtraction:
[
6 – 4 = 2
]
Conclusion
Therefore, the simplified expression yields:
[
\sqrt{36} – 2^2 = 2
]
Answer Choices
Given the answer choices of 2, 10, 16, and 32, the correct answer is 2.
Explanation of the Process
In simplifying expressions involving radicals and exponents, it’s crucial to follow the order of operations. Start by addressing any operations inside parentheses, followed by exponents and roots, and finally proceed with multiplication, division, addition, and subtraction. This ensures that each part of the expression is evaluated correctly and consistently.
In our specific problem, we tackled the square root and the exponent before proceeding to the subtraction. This systematic approach not only leads to the correct answer but also minimizes the chances of error, especially in more complex expressions. Recognizing the significance of each step is fundamental in algebra, as it lays the groundwork for solving equations and understanding more advanced mathematical concepts. This process demonstrates how foundational skills in arithmetic can be applied to more intricate problems, reinforcing the importance of mastering basic operations.