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Chapter 7: Problem 60

Simplify each root. $$ \sqrt{(-13)^{2}} $$

Short Answer

Expert verified
\( 13 \)

Step by step solution

01

Identify the Expression Inside the Root

The expression given is \ \ \(\sqrt{(-13)^{2}}\). First, look inside the square root to understand the expression you need to simplify.
02

Evaluate the Power

Next, evaluate \((-13)^{2}\). This means \(-13\) multiplied by itself. \ \ \( (-13) \times (-13) = 169 \).
03

Simplify the Square Root

Take the square root of the resulting value. \ \ \( \sqrt{169} = 13 \).

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Key Concepts

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

Evaluating Powers
Understanding how to evaluate powers is essential in various math problems. When you see an expression like \((-13)^{2}\), it means you need to multiply -13 by itself.
Here's how it works: \((-13) \times (-13)\). Multiplying two negative numbers gives a positive result. Thus, \( -13 \times -13 = 169\).
It's very important to remember the rules for signs:
  • Negative times negative is positive.
  • Negative times positive is negative.
  • Positive times positive is positive.
Once you evaluate the power, you proceed to the next steps in simplification.
Square Roots
A square root represents a number that, when multiplied by itself, gives the original number. For example, the square root of 169 is 13 because \(13 \times 13 = 169\).
In the given problem, after evaluating \((-13)^{2}\) to get 169, you then need to find \(\sqrt{169}\).
Here are some key points about square roots:
  • If \(\text{n}^2 = a\), then \(\text{n}\) is a square root of \(\text{a}\).
  • Square roots of positive numbers are always positive.
  • \
Arithmetic Operations
Arithmetic operations are the basic building blocks of math, including addition, subtraction, multiplication, and division.
For example, in simplifying square roots, multiplication and subsequent operations play a role.
Let's break down the operations in the given problem:
  • First, you evaluated the power: \((-13) \times (-13) = 169\).
  • Next, you simplified: \(\text{鈭�169} = 13\).
Understanding these simple arithmetic rules helps you navigate through more complicated math problems with ease.
Practice these operations regularly to build a strong math foundation.

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Most popular questions from this chapter

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