#AP SAT (Digital) Math: Radical, Rational, and Absolute Value Equations 🚀

Hey there, future math whiz! 👋 Let's tackle those tricky radical, rational, and absolute value equations. They might seem daunting, but with the right strategies, you'll be solving them like a pro in no time. This guide is your go-to resource for a quick review before the big day. Let’s get started!

#Radical Equations

Radical equations involve variables inside a radical (like a square root or cube root). Here's how to conquer them:

#Isolating the Radical

• Goal: Get the radical term all by itself on one side of the equation. Think of it as giving the radical its own personal space. 🧘
• Use inverse operations (addition, subtraction, multiplication, division) to move other terms away from the radical. Remember, what you do to one side, you must do to the other!

#Eliminating the Radical

• Key Step: Raise both sides of the equation to the power that matches the root's index. For example:
  • Square both sides for a square root (√) equation.
  • Cube both sides for a cube root (∛) equation.
  • Raise to the nth power for an nth root equation.
• This gets rid of the radical, leaving you with a simpler equation to solve. 🎉
• Solve the resulting equation using methods for linear or quadratic equations.

#Verifying Solutions

• Crucial Step: Always plug your solutions back into the original equation. This helps you spot any extraneous solutions (solutions that don't actually work in the original equation).
• Extraneous solutions often pop up when squaring or cubing both sides.