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Chapter 2: Problem 21

For Exercises \(1-74,\) simplify. $$\sqrt{25}-\sqrt{9}$$

Short Answer

Expert verified
Question: Simplify the expression \(\sqrt{25} - \sqrt{9}\). Answer: The simplified expression is 2.

Step by step solution

01

Find the square root of 25

To find the square root of 25, we look for a number that, when multiplied by itself, gives us 25. That number is 5. So, \(\sqrt{25} = 5\).
02

Find the square root of 9

To find the square root of 9, we look for a number that, when multiplied by itself, gives us 9. That number is 3. So, \(\sqrt{9} = 3\).
03

Subtract the square roots

Now that we have found the square root of each number, we can subtract them. So the simplified expression becomes: $$\sqrt{25} - \sqrt{9} = 5 - 3 = 2$$ The simplified expression is 2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions
Simplifying expressions often involves breaking down a complex problem into simpler parts. In this exercise, we worked on simplifying the expression \( \sqrt{25} - \sqrt{9} \). To simplify this expression, our first step was to find the square roots of both numbers under the radical sign.
  • For \( \sqrt{25} \), the square root is 5, because 5 multiplied by itself gives 25.
  • For \( \sqrt{9} \), the square root is 3, because 3 multiplied by itself gives 9.
After determining the square roots, the next step is to perform the subtraction: 5 minus 3. Simplifying these steps highlights how manageable expressions can become when broken down into smaller, more digestible parts.
Basic Arithmetic
Basic arithmetic is fundamental in understanding mathematical expressions and includes operations like addition, subtraction, multiplication, and division.
These operations are the building blocks of more complicated equations and expressions. When dealing with square roots in the given exercise, after finding and simplifying them (\(5\) and \(3\)), subtraction was used:
  • Subtraction is taking one number away from another, which in this case is \(5 - 3 = 2\).
This simple operation helped reach the final simplified result. Understanding basic arithmetic helps in tackling larger problems efficiently by focusing on solving smaller pieces first.
Prealgebra Concepts
Prealgebra introduces concepts that act as a crucial foundation for more advanced math topics.
Understanding square roots and the basics of simplifying expressions are central to prealgebra. In the exercise, recognizing the need to simplify \( \sqrt{25} \) and \( \sqrt{9} \) was essential.
  • Square roots allow us to revert squares back into their original numbers, which is key in simplifying expressions.
  • Handling expressions like \( \sqrt{25} - \sqrt{9} \) and breaking them into smaller arithmetic parts is a vital prealgebra skill.
These skills form the groundwork for future algebraic concepts, enabling students to handle more complex equations with confidence as they progress.

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