PRINCIPAL SQUARE ROOT

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.

Quick Summary

The principal square root is always non-negative.
Every perfect square number has two square roots (positive and negative), but only the positive one is considered the principal square root.
The concept of principal square root is only valid for positive real numbers and not valid for negative real numbers.

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🍎 Teacher Insights

Emphasize the 'non-negative' aspect. Use examples to differentiate between square roots and principal square roots. Address the common mistake of including the negative root.

🎓 Prerequisites

Basic Arithmetic
Understanding of Squares
Positive and Negative Numbers

Check Your Knowledge

Q1: What is the principal square root of 25?

A. 5 B. -5 C. ±5 D. 12.5

Q2: Which of the following is the principal square root of 49?

A. -7 B. 7 C. ±7 D. None of the above

Frequently Asked Questions

Q: What is the principal square root of 9?
A: The principal square root of 9 is 3, not -3.

Q: Can a principal square root be negative?
A: No, the principal square root is always non-negative.