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Chapter 1: Problem 665

Simplify. $$ \sqrt{100} $$

Short Answer

Expert verified
The simplified form of \sqrt{100} is 10.

Step by step solution

01

Identify the expression under the square root

The expression inside the square root is 100.
02

Recognize if the number is a perfect square

100 is a perfect square because it can be expressed as the square of an integer.
03

Find the square root of the number

The square root of 100 is 10, since 10 multiplied by 10 equals 100.

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Key Concepts

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

Perfect Squares
A perfect square is a number that can be expressed as the product of an integer with itself. Understanding perfect squares is crucial when simplifying square roots. For example, 100 is a perfect square because it can be written as 10 脳 10. Here are some more examples of perfect squares:
  • 1 (since 1 脳 1 = 1)
  • 4 (since 2 脳 2 = 4)
  • 9 (since 3 脳 3 = 9)
  • 16 (since 4 脳 4 = 16)
Knowing perfect squares helps you quickly identify if a number has an integer as its square root. This will significantly simplify your calculations!
Square Root
The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, the square root of 100 is 10, as 10 脳 10 equals 100. To denote the square root of a number, we use the radical sign (鈭�).
Here are some key things to remember about square roots:
  • Only non-negative numbers have real number square roots since you need a positive number to get a positive product.
  • The square root of a perfect square is always an integer.
  • You can simplify square roots by identifying perfect squares.
For example: \(\text{If you have } \sqrt{100}, \text{ recognize that } 100 \text{ is a perfect square (10 脳 10). Thus, } \sqrt{100} = 10.\)
Integer Multiplication
Knowing how to multiply integers convincingly is necessary to understand perfect squares and square roots. Integer multiplication is simply combining two whole numbers in a way that follows the arithmetic rules.
Important facts about integer multiplication include:
  • The product of two positive integers is positive.
  • The product of two negative integers is also positive.
  • The product of a positive integer and a negative integer is negative.
  • Multiplying any integer by zero results in zero.
An example of integer multiplication can be seen in the context of perfect squares: 10 脳 10 = 100. Understanding this helps you to identify perfect squares and simplify square roots efficiently.

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