(Order of Operations with Radicals MC)

Simplify the quantity 12 minus three fifths times the square root of 25 end quantity squared plus the quantity 2 minus 4 end quantity squared.

 a
1,804

 b
814

 c
85

 d
18



Let's simplify the expression step by step using the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

The expression is:

\[
\left( 12 - \frac{3}{5} \times \sqrt{25} \right)^2 + (2 - 4)^2
\]

### Step 1: Simplify the square roots
We know that \(\sqrt{25} = 5\). Substituting this value in, the expression becomes:

\[
\left( 12 - \frac{3}{5} \times 5 \right)^2 + (2 - 4)^2
\]

### Step 2: Simplify the multiplication
\[
\frac{3}{5} \times 5 = 3
\]
Now the expression is:

\[
\left( 12 - 3 \right)^2 + (2 - 4)^2
\]

### Step 3: Perform the subtraction inside the parentheses
\[
12 - 3 = 9
\]
\[
2 - 4 = -2
\]
Now the expression is:

\[
(9)^2 + (-2)^2
\]

### Step 4: Apply the exponents
\[
9^2 = 81
\]
\[
(-2)^2 = 4
\]
Now the expression is:

\[
81 + 4
\]

### Step 5: Final addition
\[
81 + 4 = 85
\]

The simplified result is **85**.

### Correct Answer:  
**c) 85**

---

Would you like further clarification or details on any step? Here are some related questions to explore:

1. How do radicals affect the order of operations in more complex expressions?
2. Can a square root ever result in a negative number?
3. What happens if you multiply different types of radicals?
4. How would the process change with cube roots or other higher roots?
5. Why does squaring a negative number result in a positive value?

**Tip**: Always simplify expressions inside parentheses first, especially when dealing with radicals or exponents.

Simplify the quantity 12 minus three fifths times the square root of 25 end quantity squared plus the quantity 2 minus 4 end quantity squared.

This step-by-step guide simplifies the expression 12 - 3/5 * √25 + (2 - 4)^2 using order of operations and radicals. Learn how to handle exponents, subtraction, and multiplication with square roots, perfect for Grades 7-10 math students.

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