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Principal Value of a Square Root

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Principal Value of a Square Root

Study Guide

Key Definition

The principal square root of a number $b$ is the non-negative solution of $x^2 = b$, denoted as $\sqrt{b}$.

Important Notes

The principal square root is always non-negative.
Every positive number has two square roots: positive and negative.
The principal square root of $25$ is $5$.
The equation $x^2 = 100$ has roots $10$ and $-10$.
Simplifying $\sqrt{36}$ results in $6$.
For negative numbers b<0, there is no real principal square root.

Mathematical Notation

$\sqrt{x}$ denotes the principal square root of $x$

$x^2$ means $x$ squared

Remember to use proper notation when solving problems

Why It Works

Understanding the principal square root involves recognizing that it provides the non-negative solution to $x^2 = b$, ensuring consistency in mathematical calculations.

Remember

The principal square root is the positive number that, when squared, returns the original number $b$.

Quick Reference

Principal Square Root:$\sqrt{b}$

Understanding Principal Value of a Square Root

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Video explanation of this concept

Beginner

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Beginner Explanation

The principal square root of a non-negative number $b$ is the non-negative number that squares to $b$; for example, $\sqrt{9}$ = $3$ because $3^2 = 9$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the principal square root of $49$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A skateboard ramp is designed with a height of $9$ feet. Find the principal square root of the height.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If the area of a square is $64$ square units, what is the side length?

Challenge Quiz

Single Choice Quiz

Advanced

What is the principal square root of $0.25$?

Recap

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