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Square roots are a fundamental concept in mathematics. They represent a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 multiplied by 3 equals 9.

Square roots are written with the radical symbol, such as in \( \sqrt{9} \ \). When you see this symbol, it means you are looking for a number which, when squared, results in the number inside the radical.

Learning to find square roots can help you solve various types of mathematical problems more easily.

• The square root of 1 is 1.
• The square root of 4 is 2.
• The square root of 9 is 3.
• The square root of 16 is 4.
• The square root of 25 is 5.

Square roots can be applied across different areas such as algebra, geometry, and different real-world scenarios.

Basic arithmetic involves the fundamental operations of mathematics: addition, subtraction, multiplication, and division. In this exercise, we focus on addition.

To add numbers, place them side by side with the addition symbol in between. For instance, in our problem, after simplifying \( \sqrt{9} \ \) to 3 and \( \sqrt{16} \ \) to 4, we need to add these two numbers:

\( 3 + 4 \).

Addition follows straightforward rules:

• Combine the numbers to get a sum.
• Order doesn’t matter: 3 + 4 = 4 + 3.

Using these simple rules, we find that \(3 + 4 = 7\). Basic arithmetic is an essential skill in both daily life and more advanced mathematical concepts.

Simplification steps are procedures applied to break down more complex expressions into simpler, more manageable components. These steps make it easier to understand and solve problems.

In our given example, we were tasked to simplify \( \sqrt{9} + \sqrt{16} \ \). Here’s how we approached this task:

Step 1: Simplify \( \sqrt{9} \ \)
Look at the square root of 9. We find that \( \sqrt{9} = 3 \ \).

Step 2: Simplify \( \sqrt{16} \ \)
Similarly, find the square root of 16. We find that \( \sqrt{16} = 4 \ \).

Step 3: Add the simplified terms together
Combine the results from steps 1 and 2. So, \( 3 + 4 = 7 \).

By following these simplification steps, complex problems become easier to manage. Practice these steps regularly to gain confidence and proficiency.