뒤로Square Roots and Their Properties
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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.
Principal Root: The positive square root of a number. For example, the principal root of 9 is 3.
Negative Root: The negative square root of a number. For example, the negative root of 9 is -3.
General Principle: If and , then .
Examples
Example 1: Find the square roots of 9.
Test: and
Therefore, the square roots of 9 are 3 and -3.
Example 2: Find the square roots of 16.
Test: and
Therefore, the square roots of 16 are 4 and -4.
Key Formula
For any positive real number :
Additional info:
Square roots are fundamental in algebra and are used in solving quadratic equations, simplifying expressions, and understanding the properties of exponents.
For negative numbers, the square root is not a real number; instead, it is an imaginary number (e.g., ).
