뒤로Square Roots and Their Properties
스터디 가이드 - 스마트 노트
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Square Roots
Definition and Properties
The square root of a number is a value that, when multiplied by itself, yields the original number. For any positive real number, there are always two square roots: one positive (the principal root) and one negative.
Definition: If , then is a square root of .
Principal Root: The positive square root is called the principal root.
Negative Root: The negative square root is also valid, since .
Examples
Example: To find the square roots of 9, solve .
Testing :
Testing :
Therefore, the square roots of 9 are 3 and -3.
General Principle
For any positive real number , the equation has two solutions: and .
For example, yields and .
Key Formula
The square root of is denoted as .
Both and are square roots of .
Additional info: This topic is foundational for College Algebra, especially in solving quadratic equations and understanding properties of real numbers.
