/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 59 Simplify each root. $$ \sqrt... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 59

Simplify each root. $$ \sqrt{(-10)^{2}} $$

Short Answer

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Step by step solution

01

- Understand the Problem

The goal is to simplify the expression \(\u221A{(-10)^{2}}\). This involves finding the square root of \((-10)^{2}\).
02

- Evaluate the Exponent

Calculate \((-10)^{2}\): \((-10)^{2} = (-10) \times (-10) = 100\).
03

- Simplify the Square Root

Find the square root of 100: \(\u221A{100} = 10\).

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Key Concepts

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

Square Roots
A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 100 is 10 because 10 multiplied by itself (10 \times 10) equals 100. The symbol for the square root is \(\sqrt{}\).
To simplify a square root:
Find the prime factors of the number inside the square root.
Pair the factors in groups of two.
Bring one factor out of each pair.
In our exercise, we simplified \(\sqrt{(-10)^{2}}\) by first evaluating \((-10)^2\) to get 100, then finding the square root of 100 to get 10.
Exponents
Exponents are a way to express repeated multiplication of the same number. The expression \((-10)^2\) means that -10 is multiplied by itself: \(-10 \times -10\). This results in 100 because multiplying two negative numbers yields a positive result. Exponents make calculations more concise and are an essential part of algebra.
Here are some rules for working with exponents:
  • Anything raised to the power of zero is 1: \(a^0 = 1\).
  • Multiplying powers with the same base: \(a^m \times a^n = a^{m+n}\).
  • Dividing powers with the same base: \(a^m \div a^n = a^{m-n}\).
  • Raising a power to another power: \( (a^m)^n = a^{mn}\).
In our exercise, \((-10)^2\) was evaluated to get 100, which then made it easy to take the square root.
Algebraic Simplification
Algebraic simplification is the process of making expressions easier to work with by combining like terms and applying mathematical operations. It helps to understand the problem better and find the solution more efficiently. Here are some tips for simplifying expressions:
  • Combine like terms: terms with the same variable raised to the same power.
  • Use distributive property to eliminate parentheses: \(a(b + c) = ab + ac\).
  • Factor when possible to simplify complex expressions.
In the given exercise, we simplified the expression \( \sqrt{(-10)^2}\) step-by-step:
First, find the value of \((-10)^2\), which is 100.
Then, take the square root of 100, which results in 10.
This step-by-step approach ensures complete simplification and a clear final result.

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Most popular questions from this chapter

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