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Principal Square Root

Definition Of Principal Square Root

The non-negative (positive) square root of a number is called its Principal Square Root.

More About Principal Square Root

Every perfect square number has two square roots (positive and negative).
The concept of principal square root is only valid for positive real numbers and not valid for negative real numbers.

Video Examples: Principal Square Roots

Example of Principal Square Root

Square roots of 16 are + 4 and - 4.
4 is the positive square root of 16.
So, 4 is the principal square root of 16. 

Solved Example on Principal Square Root

Ques: Identify the principal square root of 64.

Choices:

A. 8
B. - 8
C. - 4
D. 4
Correct Answer: A

Solution:

Step 1: The positive square root of a number is called its principal square root.
Step 2: Square roots of 64 are + 8 and - 8.
Step 3: 8 is the positive square root of 64.
Step 4: So, 8 is the principal square root of 64.