/*! 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 10 Evaluate or simplify each expres... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 10

Evaluate or simplify each expression. (Assume \(x \geq 0 .)\) $$-\sqrt{36}$$

Short Answer

Expert verified
-6

Step by step solution

01

Understand the Square Root

The square root function, denoted by \(\backslashsqrt{...}\), finds a number which, when multiplied by itself, equals the given value. For example, \( \backslashsqrt{36} \) means finding a number that when squared equals 36.
02

Calculate the Square Root

Calculate the square root of 36. \( \backslashsqrt{36} = 6 \) because 6 * 6 = 36.
03

Apply the Negative Sign

The expression \( -\backslashsqrt{36} \) includes a negative sign. So, we take the square root found in the previous step and apply the negative sign: -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.

Square Root
The square root is an important concept in mathematics. It's a value that, when multiplied by itself, gives the original number.
For instance, the square root of 36 is the number that, when squared, equals 36. In our exercise, we write this as \( \sqrt{36} \).
The answer to this is 6, because \( 6 \times 6 = 36 \).
If you're dealing with perfect squares like 36, finding the square root is straightforward. For non-perfect squares, you may need a calculator.
Remember, square root only deals with non-negative numbers, especially when we assume \( x \geq 0 \) as stated in the problem.
Negative Sign
A negative sign in front of the square root changes the result's sign.
In our problem, we have \( -\sqrt{36} \). Here, we first calculate \( \sqrt{36} \), which is 6.
Then we apply the negative sign, resulting in -6.
This is important: the negative sign comes after finding the square root. It's a two-step process:
  • First, find the square root.

  • Second, apply the negative sign.
This step-by-step process ensures you correctly evaluate the expression.
Multiplication
Multiplication and square roots often go hand-in-hand.
In our example, to find \( \sqrt{36} \), we used the fact that 6 multiplied by itself equals 36.
Multiplication is how you verify the square root.
Let's break it down:
  • We know 6 times 6 (or \( 6 \times 6 \)) equals 36.

  • So, the square root of 36 must be 6.
In mathematical notation, this is written as \( \sqrt{36} = 6 \) because \( 6 \times 6 = 36 \).
This way, multiplication is crucial for understanding and confirming the results of square roots.

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 each of the following, perform the indicated operations and simplify as completely as possible. Assume all variables appearing under radical signs are non negative. $$\sqrt{28}-\sqrt{7}$$

Use a calculator to find \(\sqrt{80} .\) Then simplify \(\sqrt{80}\) and again use the calculator to compute the value of the simplified form. Are the results the same? Should they be?

Perform the indicated operations. Simplify all answers as completely as possible. Assume that all variables appearing under radical signs are nonnegative. $$\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}$$

Factor the given expression as completely as possible. $$a^{2}+6 a-40$$

Perform the indicated operations and simplify. $$\text { Solve for } x, \quad \frac{6}{x-6}=\frac{2}{x-2}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.