Problem 31 - Fundamentals of Mathematics

Question

Find each value. Check each result with a calculator. \(\sqrt{9}+14\)

Step-by-Step Solution

Answer

The result is 17.

Step 1: Simplify the Square Root

To find the value of \( \sqrt{9} \), you need to calculate which number, when multiplied by itself, gives 9. The number that satisfies this is 3, because \( 3 \times 3 = 9 \). Thus, \( \sqrt{9} = 3 \).

Step 2: Perform the Addition

Now that you have simplified \( \sqrt{9} \) to 3, you can add this value to 14. This gives you: \( 3 + 14 = 17 \).

Step 3: Verify with a Calculator

Use a calculator to perform the operations. First, find \( \sqrt{9} \) to confirm it's 3, and then calculate \( 3 + 14 \). You will see that the result is indeed 17.

Key Concepts

Understanding Square Roots

A square root is a number that, when multiplied by itself, gives the original number. It's represented by the symbol \( \sqrt{} \). For example, \( \sqrt{9} \) asks us, "What number times itself equals 9?" The answer is 3, since \( 3 \times 3 = 9 \).

Square roots are essential in mathematics, helping us solve equations and understand geometric concepts. Recognizing perfect squares—numbers like 9, 16, and 25 that have whole numbers as square roots—is particularly useful.

• They simplify many algebraic expressions.
• They allow us to calculate distances, areas, and more in geometry.

Knowing how to work with square roots can also help simplify your calculations, making complex problems more manageable.

The Role of Basic Arithmetic in Problems

Basic arithmetic involves the simple operations of addition, subtraction, multiplication, and division. When dealing with mathematics, these operations form the foundational skills needed for problem-solving.

In our example, once we simplified \( \sqrt{9} \) to 3, we proceed with another basic arithmetic operation: addition. We needed to add 3 to 14 to find the final result.

• Addition combines values to form a total or sum.
• Subtraction finds the difference between numbers.
• Multiplication calculates the total of one number taken multiple times.
• Division splits a number into equal parts.

Mastery of these arithmetic operations allows you to tackle larger, more intricate mathematical challenges with ease.

Step-by-Step Math Solutions

Following a step-by-step approach in solving math problems ensures accuracy and clarity. Breaking a problem down simplifies complex concepts into understandable chunks.

For instance, our exercise involved:

• Step 1: Simplifying \( \sqrt{9} \) to 3 by finding what number squared equals 9.
• Step 2: Using basic arithmetic to add the simplified square root to 14, resulting in 17.
• Step 3: Verifying the solution with a calculator to ensure correctness.

Each step builds upon the other, reinforcing the understanding of both basic arithmetic and more complex operations like square roots.