/*! 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 1 Rewrite the number without radic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 1

Rewrite the number without radicals or exponents.. $$ \sqrt{81} $$

Short Answer

Expert verified
The simplified expression without radicals or exponents is \( 9 \).

Step by step solution

01

Identify the square root of 81

The square root of 81 is a number that, when multiplied by itself, equals 81. In this case, it is 9 because \( 9 * 9 = 81 \).
02

Rewrite the expression without radicals or exponents

Since the square root of 81 is 9, we can rewrite the expression \( \sqrt{81} \) as 9. So, the simplified expression without radicals or exponents is: \( 9 \)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Square Roots
Square roots are mathematical functions symbolized by the radical sign \( \sqrt{ } \). They represent a value that, when multiplied by itself, gives the original number. For example, the square root of 81 is 9 because \( 9 \times 9 = 81 \).
Square roots are fundamental in solving equations and simplifying mathematical expressions. They are often used to "undo" the process of squaring a number.
  • This means if you have a number squared, taking the square root returns the number to its original form.
  • Mathematically, it is expressed as \( x^2 \rightarrow x \) when \( \sqrt{ } \) is applied.
Knowing how to compute square roots is crucial in many areas, including geometry and algebra. There are various methods to find square roots, such as estimation, the use of calculators, or memorizing common square roots like \( \sqrt{81} = 9 \).
Mathematical Expressions
A mathematical expression is a combination of numbers, operators, symbols, and sometimes variables, all arranged in a meaningful way to represent a mathematical concept or problem.
Expressions can vary in complexity, from simple numerical identities like \( 4 + 3 \) to complex algebraic equations.
In the context of simplifying radicals, expressions often contain square roots or exponents.
  • Simplifying these expressions involves using mathematical rules and operations to break them down into simpler forms.
  • For example, converting \( \sqrt{81} \) to 9 is a simplification process that eliminates the radical symbol.
Understanding how to manipulate and rewrite expressions is essential for solving equations and completing algebraic operations.
Number Operations
Number operations are the building blocks of arithmetic and involve addition, subtraction, multiplication, and division. They play a critical role in manipulating numbers and solving problems.
Each operation has its unique properties and rules that govern how numbers are combined and transformed.
  • For instance, multiplication is repeated addition, and division is the inverse of multiplication.
  • Understanding how to perform these operations seamlessly is crucial for simplifying radicals and solving equations.
When dealing with square roots like \( \sqrt{81} \), multiplication comes into play because the square root itself represents repeated multiplication: \( 9 \times 9 = 81 \).
This knowledge assists in recognizing patterns and manipulating expressions efficiently. Mastery of number operations is foundational to further mathematical learning and problem-solving.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Perform the indicated operations and simplify. \(\frac{t}{t^{2}+t-2}-\frac{2 t-1}{2 t^{2}+3 t-2}\)

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, explain why or give an example to show why it is false. If \(b^{2}-4 a c \neq 0\) and \(a \neq 0\), then \(a x^{2}+b x+c=0\) has two distinct real roots, or it has no real roots at all.

Perform the indicated operations and simplify. \(\frac{a x+b y}{a x-b x}+\frac{a y-b x}{b y-a y}\)

Determine whether the statement is true for all real numbers \(a\) and \(b\). $$ |a+1|=|a|+1 $$

Solve the equation by using the quadratic formula. $$ 8(2 m+3)^{2}+14(2 m+3)-15=0 $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.