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Chapter 5: Problem 661

In the following exercises, simplify. $$ \sqrt{144} $$

Short Answer

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Step by step solution

01

Identify the Operation

Recognize that the operation needed to simplify is finding the square root of 144.
02

Recall the Definition of Square Root

A square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms, for a number x, its square root is denoted as \(\backslash \textbackslash sqrt{x}\).
03

Determine the Square Root

Determine what number, when multiplied by itself, equals 144. Multiply 12 by 12: \(\backslash textbackslash 12 \backslash textbackslash times 12 = 144\).
04

Conclude the Simplification

Conclude that the square root of 144 is 12 because \(\ sqrt{144} = 12 \).

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Key Concepts

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

Square Root Definition
A key part of simplifying square roots is understanding what a square root actually is. The square root of a number is a value that, when multiplied by itself, gives the original number.

For example, if you have \(\backslash sqrt{x}\) where x is 144, you need to find a number that, when squared (multiplied by itself), equals 144.
The equation would look like this: \textbackslash 12 \backslash textbackslash times 12 = 144.\
Multiplication
To identify the square root, you need to understand multiplication. Multiplication is when you take one number and add it to itself a certain number of times.

For example, when you say 12 times 12, you are saying 12 multiplied by 12. This is called squaring the number. In our case:
\[12 \times 12 = 144 \]
This means 12 is the square root of 144.
Simplification Steps
Simplifying square roots involves a few clear steps:

  • Step 1: Identify the Operation. Recognize that you're finding the square root of the given number.
  • Step 2: Recall the Definition. Remember that the square root of a number is a value that, when multiplied by itself, gives that number.
  • Step 3: Determine the Square Root. Find what number multiplied by itself equals the original number, in this case, 144. For example, 12 脳 12 = 144.
  • Step 4: Conclude the Simplification. Finally, determine that the square root of 144 is 12.

By following these steps, you can simplify square roots consistently and accurately.

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Most popular questions from this chapter

The parking lot at the airport charges \(\$ 0.75\) for every 15 minutes. (a) How much does it cost to park for 1 hour? (b) Explain how you got your answer to part (a). Was your reasoning based on the unit cost or did you use another method?

In the following exercises, order each of the following pairs of numbers, using < or >. $$0.415 \underline\quad 0.41$$

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