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Chapter 8: Problem 30

Simplify the squares and square roots. $$\sqrt{25}$$

Short Answer

Expert verified
\( \sqrt{25} = 5 \)

Step by step solution

01

Identify the Square Root

Recognize that the expression is asking for the square root of 25, written as \(\sqrt{25}\)\.
02

Find the Square Root

Determine which number, when multiplied by itself, equals 25. In this case, \(5 \times 5 = 25\), so the square root of 25 is 5.
03

Write the Final Answer

Write the simplified result: \(\sqrt{25} = 5\)\.

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Key Concepts

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

Simplifying Square Roots
Simplifying square roots may seem intimidating at first, but it's actually quite straightforward once you get the hang of it. The square root of a number is the value that, when multiplied by itself, gives the original number. In the case of \( \sqrt{{25}} \), we are looking to identify which number multiplied by itself equals 25.

Let's break it down further:
  • Identify the square root symbol (鈭�), which indicates that you need to find the root of the number inside it.
  • Next, determine what number times itself (squared) gives you the number under the square root symbol.
  • Once you know which number it is, you've simplified the square root!
This process can be applied to simplify any square root, making it an essential skill in mathematics.
Basic Arithmetic
Basic arithmetic is foundational for understanding more complex mathematical operations, such as simplifying square roots. It includes addition, subtraction, multiplication, and division. To simplify a square root, usually, only multiplication is directly involved.

In our example, to find \( \sqrt{{25}} \):
  • We ask ourselves, what number times itself equals 25?
  • By knowing that \(5 \times 5 = 25\), we solve the square root.
Knowing multiplication tables and simple arithmetic operations can greatly ease the process of working with square roots. Practice these operations regularly, and soon they will become second nature!
Mathematical Operations
Understanding mathematical operations is key to dealing with various problems including simplifying square roots. Let's focus on how these operations are applied in our example:

  • Multiplication: To simplify \( \sqrt{{25}} \), you need to determine that \(5\times 5\) or \(5^2 = 25\).
  • Exponents: Recognizing that 5 squared (\(5^2\)) equals 25 helps in understanding why \( \sqrt{{25}} = 5 \).
Another key point is recognizing perfect squares (numbers like 1, 4, 9, 16, 25, etc.), which makes the process of simplifying square roots quicker and more efficient. The more you familiarize yourself with these basic mathematical operations, the easier it becomes to solve similar problems in the future!

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