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Chapter 1: Problem 663

Simplify. $$ \sqrt{9} $$

Short Answer

Expert verified
The square root of 9 is 3.

Step by step solution

01

Identify the Operation

The problem requires finding the square root of 9. The square root operation seeks to find a number which, when multiplied by itself, yields the original number.
02

Find the Square Root

Determine which number multiplied by itself equals 9. There are two possible numbers, 3 and -3, because both 3 * 3 = 9 and (-3) * (-3) = 9.
03

Select the Principal Square Root

In simplification within the context of real numbers, we typically choose the positive root. Therefore, the principal square root of 9 is 3.

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Key Concepts

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

square root
A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 * 3 = 9. Simple, right? When you see the symbol \( \sqrt{} \), it tells you to find the square root of the number inside. Solving square roots is crucial in many areas of math and science. It helps us understand shapes, speed, area, and even in solving equations. So, remember, the square root of a number is like asking, 'What number can I multiply by itself to get this number?'
For practice, try to find the square root of 16 or 25 yourself!
principal square root
The principal square root is the non-negative root of a number. For instance, while both 3 and -3 are square roots of 9 because \( 3 * 3 = 9 \) and \( (-3) * (-3) = 9 \), the principal square root is always the positive one. This rule makes it easier to choose the most straightforward answer when simplifying square roots.
So, when you're asked for the square root of 9, you should always pick 3, not -3. Remember this to avoid confusion, especially in exams. If you see \( \sqrt{36} \), the principal square root is 6, not -6. It's about keeping your answers clear and consistent.
real numbers
Real numbers include all the numbers you can think of: positives, negatives, fractions, and zeros. When you're simplifying square roots, you're always dealing with real numbers. They help us describe the world around us with precision, allowing for things like measurement and calculation.
For instance, in our example, 9 is a real number, and so is its square root, 3. It's essential to understand that real numbers are everywhere. Next time you see a number, whether it鈥檚 7, -2.5, or even \( \sqrt{9} \), know that you're dealing with real numbers. They are the building blocks of most math you'll encounter.

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Most popular questions from this chapter

Insurance copayment Carrie had to have 5 fillings done. Each filling cost $$\$ 80\(. Her dental insurance required her to pay \)20 \%\( of the cost as a copay. Calculate Carrie's copay: (a) First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings. (b) Next, by multiplying \)[5(0.20)](80)\( (c) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \)5[(0.20)(80)]\( and \)(b),\( where you multiplied \)[5(0.20)](80),$$ should be equal?

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