Problem 7 Simplify. Assume that variables ... [FREE SOLUTION]

Chapter 7: Problem 7

Simplify. Assume that variables represent positive real numbers. $$ -\sqrt{36} $$

Short Answer

Expert verified

The simplified expression is $-6$.

Step by step solution

Understand the problem

The problem asks us to simplify the expression $-\sqrt{36}$.The symbol $-$ indicates a negative, and $\sqrt{36}$ stands for the square root of 36.

Simplify the square root

Calculate the square root of 36. Since 36 is a perfect square,$\sqrt{36} = 6$.

Apply the negative sign

Now, apply the negative sign in front of the square root result:$-6$.This is the simplified form of the given expression.

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.

Understanding Square Roots

Square roots are a fundamental idea in mathematics. When we talk about the square root of a number, we're looking for a value that, when multiplied by itself, gives us the original number.
Take for instance, the square root of 36. We ask: what number times itself equals 36? The answer is 6, because $6 \times 6 = 36$.
When you see the symbol $\sqrt{}$, it's asking you to find this special number. This process is very helpful when simplifying expressions. Knowing your perfect squares can make finding square roots quicker and easier.

Recognizing Perfect Squares

Perfect squares are numbers that have exact whole numbers as their square roots. Being familiar with perfect squares is invaluable when dealing with square roots. For example, numbers like 4, 9, 16, 25, 36, and 49 are a few early perfect squares.

4 is a perfect square because $2 \times 2 = 4$
9 is a perfect square because $3 \times 3 = 9$
36 is a perfect square because $6 \times 6 = 36$

Knowing perfect squares speeds up the simplification of square roots since they directly result in whole numbers without the need for tricky calculations.

Handling Negative Numbers

Negative numbers can seem daunting at first, but they're straightforward once you break down what they mean. A negative sign basically indicates that a number is less than zero.
In the context of simplifying expressions, the negative sign in front of a square root means you're taking the opposite, or negating, the positive square root's result.
So, for $-\sqrt{36}$, once you realize that $\sqrt{36} = 6$, you simply apply the negative sign and say the simplified expression is $-6$.
This step solidifies your understanding of both square roots and how negatives modify numbers.

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify. Assume that variables represent positive real numbers. $$ -\sqrt{36} $$

Short Answer

Step by step solution

Understand the problem

Simplify the square root

Apply the negative sign

Key Concepts

Understanding Square Roots

Recognizing Perfect Squares

Handling Negative Numbers

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Calculus

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.