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Chapter 5: Problem 533

What is the difference between \(9^{2}\) and \(\sqrt{9} ?\)

Short Answer

Expert verified
The difference is 78.

Step by step solution

01

Calculate the square of 9

First, calculate the square of 9. This is done by multiplying 9 by itself: \[ 9^2 = 9 \times 9 = 81 \]
02

Calculate the square root of 9

Next, find the square root of 9. The square root of 9 is a number which, when multiplied by itself, gives 9: \[ \ \ \, \ \sqrt{9} = 3 \]
03

Find the difference

Finally, subtract the square root of 9 from the square of 9 to get the difference: \[ 81 - 3 = 78 \]

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Key Concepts

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

squares
A square in mathematics means multiplying a number by itself. For example, the square of 9, written as \(9^2\), is calculated by multiplying 9 by 9: \[9^2 = 9 \times 9 = 81\]. Squaring has a wide range of applications including geometry, physics, and other areas where growth patterns need to be modeled. Remember that squaring a positive or negative number always results in a positive number because multiplying two negative numbers also yields a positive result.
square roots
The square root of a number is the value that, when multiplied by itself, gives the original number. For instance, the square root of 9 is 3 because \[3 \times 3 = 9\]. Notation for square roots uses the radical symbol \(\sqrt{}\). So, \(\sqrt{9}\) means the square root of 9, which equals 3. Square roots are fundamental in various fields like probability, statistics, and even in everyday problems that require understanding inverse operations to squaring.
differences
To find the difference means to subtract one number from another. In this context, it involves subtracting the square root of 9 from the square of 9. Calculating the difference between \(\sqrt{9}\) and \(9^2\) helps to understand both operations better. So, the difference is: \[81 - 3 = 78\]. This calculation can be useful for comparing different forms of numbers and understanding their relationships.

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Most popular questions from this chapter

Sales Tax Jennifer bought a \(\$ 1,038.99\) dining room set for her home in Cincinnati. She calculated the sales tax to be exactly \(\$ 67.53435\) . Round the sales tax to the nearest (a) penny (b) dollar.

In the following exercises, divide. $$ 9 \div 0.045 $$

In the following exercises, name each decimal. $$ 0.8 $$

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