/*! 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 489 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 489

In the following exercises, simplify. $$ \sqrt{36} $$

Short Answer

Expert verified
鈭�36 = 6

Step by step solution

01

Recognize the square root

The problem involves finding the square root of 36, written as \(\text{鈭�36}\).
02

Identify perfect squares

Notice that 36 is a perfect square because it is the result of multiplying 6 by itself. Mathematically, this can be written as \[6 \times 6 = 36\].
03

Simplify the square root

Since 36 is a perfect square, take the square root of 36 to get 6. Therefore, \(\text{鈭�36} = 6\).

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.

Perfect Squares
To simplify a square root, it's crucial to understand the concept of perfect squares. A perfect square is a number that can be expressed as the product of an integer with itself. For example, the number 36 is a perfect square because it can be written as \[6 \times 6 = 36\]. Here, 6 is the integer that was multiplied by itself. Recognizing perfect squares helps simplify square root problems.
Common perfect squares include:
  • 1 (1 \times 1)
  • 4 (2 \times 2)
  • 9 (3 \times 3)
  • 16 (4 \times 4)
  • 25 (5 \times 5)
  • 36 (6 \times 6)
Identifying these perfect squares will make it easier to solve square root problems quickly and accurately.
Square Root
The square root operation is used to find a number which, when multiplied by itself, gives the original number. Symbolically, the square root of a number \(x\) is represented as \(\sqrt{x}\). For example, the square root of 36 is represented as \(\sqrt{36}\).
In this instance, since we know that 36 is a perfect square, the square root of 36 is 6. This is because 6 \( \times\ 6 = 36 \).
The square root simplifies the original number鈥檚 value to an easily manageable form. Simplifying square roots is a fundamental skill in algebra that aids in solving various mathematical problems, including those involving quadratic equations and geometry.
Simplification Steps
Simplifying square roots involves a few structured steps:
  • Step 1: Recognize the square root in the problem statement. For example, \(\sqrt{36}\).
  • Step 2: Identify if the given number is a perfect square. Figure out if an integer, when multiplied by itself, gives the number under the square root. In this example, 36 is a perfect square because \(6 \times 6 = 36\).
  • Step 3: Simplify by taking the square root of the perfect square. For \(\sqrt{36}\), since 36 is a perfect square, its square root is 6.
Understanding and applying these steps will help you simplify square roots with confidence. Always start by checking for perfect squares, then follow the simplification process for accurate results.

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

In the following exercises, round each number to the nearest hundredth. $$3.6284$$

approximate the (a) circumference and (b) area of each circle. If measurements are given in fractions, leave answers in fraction form. radius \(=\frac{3}{8}\) yard

In the following exercises, round each number to the nearest (a) hundredth (b) tenth (c) whole number. $$84.281$$

In the following exercises, locate each number on a number line. $$0.3$$

In the following exercises, find the unit rate. Round to two decimal places, if necessary. 8.2 pounds per 3 square inches
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.