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Chapter 8: Problem 1

Quickly solve these square root problems. \(\sqrt{9}\)

Short Answer

Expert verified
The square root of 9 is 3.

Step by step solution

01

Understand the Problem

The problem asks for the square root of 9. The square root of a number is a value that, when multiplied by itself, gives the original number.
02

Identify the Square Root

The value that, when multiplied by itself, equals 9 is 3 because 3 * 3 = 9.
03

Write the Square Root

From the previous step, we know the square root of 9 is 3. So, \(\text{\(\sqrt{9} = 3\)}\)

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Key Concepts

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

Basic Arithmetic
To understand square roots, we need a good grasp of basic arithmetic. Basic arithmetic includes four primary operations: addition, subtraction, multiplication, and division. These are the building blocks of all math concepts.
For example, addition and subtraction are used to combine or separate numbers. Multiplication is repeated addition, and division is repeatedly subtracting or splitting into equal parts. Basic arithmetic is essential for understanding more complex operations such as square roots.
Multiplication
Multiplication is crucial in finding square roots. A square root of a number is a value that, when multiplied by itself, results in the original number.
For instance, to find the square root of 9, we ask what number times itself equals 9. We find that 3 * 3 = 9, so the square root of 9 is 3. Multiplication helps validate our results and ensures accuracy in finding square roots. Remember, multiplication is simply repeated addition, which can be visualized with objects or diagrams.
Number Properties
Understanding number properties is essential for solving square root problems. One key property is that square numbers are always non-negative. Another property is that square roots are inverse operations of squaring. The square of a number is that number times itself, and the square root reverses this process.
  • The square of 3 is 9 because 3 * 3 = 9.
  • The square root of 9 is 3 because the reverse process of squaring 3 gives us back 9.
These properties help us simplify and solve problems involving square roots. They are foundational concepts that make arithmetic more accessible and understandable.

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Most popular questions from this chapter

Solve for \(x\). \(\sqrt[x]{8}=2\)

Solve. \(\sqrt{32}\)

Change the radical expressions into exponential expressions. \(\sqrt[5]{7^{2}}\)

Solve the following radicals. Be careful. Some of them are undefined. \(\sqrt{-64}\)

Solve. \(2 \sqrt{3}-4 \sqrt{3}\)
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