Problem 40 - Fundamentals of Mathematics

Question

Use the order of operations to determine each value. \(\sqrt{16}+\sqrt{9}\)

Step-by-Step Solution

Answer

The value is 7.

Step 1: Understand the Order of Operations

The order of operations dictates that we first perform operations inside parentheses or radicals, then exponents, and subsequently multiplication and division, and finally addition and subtraction. Here, we must first resolve each square root before performing the addition.

Step 2: Calculate Square Roots

Calculate each square root separately. First, find the square root of 16, which is 4. Then, find the square root of 9, which is 3.

Step 3: Perform Addition

Once the square roots are calculated, add them together: \(4 + 3 = 7\).

Key Concepts

Understanding Square Roots

Square roots can sometimes seem mysterious, but they're actually quite simple once you break them down. When you see the square root symbol, like \(\sqrt{ }\), it means you are looking for a number which, when multiplied by itself, gives you the number inside the symbol. For instance, the square root of 16 is 4 because \(4 \times 4 = 16\). Similarly, the square root of 9 is 3 because \(3 \times 3 = 9\).
It's important to resolve square roots first when following the order of operations, which ensures consistency in solving mathematical expressions. Square roots fall under the category of operations that need to be addressed before you tackle addition, according to the "Please Excuse My Dear Aunt Sally" rule—or PEMDAS, which stands for Parentheses, Exponents (including square roots), Multiplication, Division, Addition, Subtraction. This ensures calculations are performed in the correct sequence.

Performing Addition

Addition is one of the simplest and most common operations in math, but it's crucial to perform it correctly. Once you've simplified any square roots or other operations that need to be done first, as dictated by the order of operations, you can then perform the addition.
This involves combining numbers by counting them together. For example, if you have already calculated that \(\sqrt{16} = 4\) and \(\sqrt{9} = 3\), you would then add these numbers together to get \(4 + 3 = 7\).
Remember that addition is the last operation you perform after all other necessary operations (like square roots in our example) have been simplified. This keeps your calculations accurate and your math functioning smoothly.

Executing Mathematical Operations

Mathematical operations can include a variety of processes, such as addition, subtraction, multiplication, division, and finding square roots, among others. These operations are at the core of basic math problem-solving.
When tackling math problems like the one given, start by determining which operations need to be performed first, consulting the order of operations to ensure accuracy. This process allows you to break down the problem into manageable steps, beginning with resolving any exponents or square roots.

• First, resolve any operations involving square roots, which can be thought of as a step within the exponent category of PEMDAS.
• Afterwards, you proceed with addition or other operations as indicated in the problem.

This approach not only helps prevent mistakes but also builds a strong foundation for handling more complex mathematical challenges in the future.