/*! 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 23 Simplify the squares and square ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 23

Simplify the squares and square roots. $$\sqrt{49}$$

Short Answer

Expert verified
7

Step by step solution

01

- Identify the Square Root

Determine the number that when multiplied by itself gives 49. This is what a square root represents.
02

- Calculate the Square Root

The number that when squared equals 49 is 7 because \[ 7 \times 7 = 49 \] Therefore, \(\sqrt{49} = 7\).
03

- Conclusion

The simplified form of \(\sqrt{49}\) is 7.

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
A square root represents a number that, when multiplied by itself, results in a specific value. For example, the square root of 49 is 7 because
\[ 7 \times 7 = 49 \]
Square roots are denoted by the radical symbol (\( \sqrt{ } \)). Many square roots of perfect squares are typically integers.
Here are a few key points about square roots:
  • If a number is a perfect square, its square root will be an integer.
  • The square root of a number \( x \) is written as \( \sqrt{x} \).
  • Understanding square roots helps solve equations and simplify expressions in algebra.
    Double-check calculations to ensure accuracy.
squares
The concept of a square is fundamental in mathematics. Squaring a number means multiplying it by itself. The result is called a perfect square.
For example:
  • The square of 7 is written as \( 7^2 \) and equals 49.
  • Similarly, \( 5^2 = 25 \).
  • Understanding squares helps in reverse operations like finding square roots.
    Practice squaring different numbers to familiarize yourself with common squares.

Knowing squares of numbers can simplify many math problems and help solve equations faster.
simplification
Simplification is the process of reducing expressions to their simplest form. In our exercise, we simplified \( \sqrt{49} \) by finding its square root.
Steps to simplify square roots:
  • Identify the square root to find which number, when squared, gives the original number.
  • Calculate the square root. For example, the square root of 49 is 7 because
    \[ 7 \times 7 = 49 \].
  • Rewrite the expression in its simplified form.

Simplification makes equations easier to understand and solve. Remember, practice is key to mastering simplification in math!

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

A recipe for punch calls for 6 c of apple juice. A bottle of juice has 2 qt. Is there enough juice in the bottle for the recipe?

Convert the temperatures by using the appropriate formula: \(F=\xi C+32\) or \(C=\frac{5}{9}(F-32)\) \(104^{\circ} \mathrm{F}=\)_____\(^{\circ} \mathrm{C}\)

Convert the temperatures by using the appropriate formula: \(F=\xi C+32\) or \(C=\frac{5}{9}(F-32)\) \(25^{\circ} \mathrm{C}=\)______\(^{\circ} \mathrm{F}\)

Cliff drives his children to their sports activities outside of school. When he drives his son to baseball practice, it is a \(6-\mathrm{km}\) round trip. When he drives his daughter to basketball practice, it is a \(1800-\mathrm{m}\) round trip. If basketball practice is 3 times a week and baseball practice is twice a week, how many kilometers does Cliff drive?

A can of paint holds 120 L. How many kiloliters are contained in 8 cans?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.