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Solving Radical Equations

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Solving Radical Equations

Study Guide

Key Definition

A radical equation is an equation in which the variable is under a radical, such as $\sqrt{x}$.

Important Notes

Isolate the radical expression before squaring both sides.
Check for extraneous solutions after solving.
Square both sides carefully to eliminate the square root.
Ensure the equation is simplified before solving.
Verify your solution by substituting it back into the original equation.

Mathematical Notation

$\sqrt{x}$ represents the square root of $x$

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Squaring both sides of an equation allows us to eliminate the square root, making it possible to solve for the variable directly.

Remember

Always check for extraneous solutions by substituting back into the original equation.

Quick Reference

Square Root Property:$\sqrt{x^2} = |x|$

Understanding Solving Radical Equations

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A radical equation is one where the variable is inside a square root, like $\sqrt{x} = 3$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve the equation $\sqrt{x} = 4$. What is $x$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If the length of a square's side is $\sqrt{x}$ meters and the area is 25 square meters, find $x$.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given $\sqrt{x+1} = x - 3$, solve for $x$.

Challenge Quiz

Single Choice Quiz

Advanced

Solve $\sqrt{2x + 3} = x - 1$.

Recap

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Review key concepts and takeaways