Solving Radical Equations - Varsity Tutors

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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 divisionRemember 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

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

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Beginner Explanation

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

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

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

A$16$B$4$C$8$D$2$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Teenager Scenario

If the length of a square's side is $\sqrt{x}$ meters and the area is 25 square meters, find $x$.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

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

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

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

A$x = 2 + \sqrt{6}$B$x = 2 - \sqrt{6}$C$x = 1$D$x = 6$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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