How To Solve Composite Radical Equations With Internal Square Roots - Algebra

TL;DR

Learn how to solve complex radical equations with square roots by taking the square of both sides and factoring.

Transcript

in this lesson we're going to talk about how to solve complex radical equations that contain square roots like this one we have a square root within the square root feel free to pause the video if you want to try this problem what I recommend doing in the first step is taking the square of both sides this will get rid of the outer square root fun f... Read More

Key Insights

• ❎ Taking the square of both sides is a key step in solving complex radical equations with internal square roots.
• 😑 Factoring the expression can help in finding the solutions.
• ✅ Checking for extraneous solutions is important to ensure the accuracy of the final answer.

Questions & Answers

Q: How do you begin solving complex radical equations with internal square roots?

To start, take the square of both sides of the equation to remove the outer square root.

Q: What is the purpose of subtracting both sides by X in the process?

Subtracting both sides by X isolates the square root of 8X on one side of the equation, making it easier to solve.

Q: How do you find the factors of an expression in order to factor it?

In this case, you can find the factors by testing numbers that multiply to give 256 and add up to -40, such as -32 and 8.

Q: How do you determine if a solution is extraneous or not?

After finding the possible solutions, substitute them back into the original equation to check if they satisfy the equation. If not, they are extraneous solutions.

Summary & Key Takeaways

• To solve complex radical equations with internal square roots, start by taking the square of both sides to eliminate the outer square root.

• Subtract both sides by X to isolate the square root of 8X on one side of the equation.

• Square both sides again to eliminate the square root, then expand and combine like terms.

• Factor the expression by grouping and set each factor equal to zero to find the possible solutions.