https://file.aiquickdraw.com/mathbot/file/1731312346393z5ls3lmp.jpg

To solve the equation involving the radical expression:

\[
\sqrt{5x} = 10
\]

we can follow these steps:

1. **Isolate the Radical:** In this equation, the radical term is already isolated on one side.

2. **Square Both Sides:** To eliminate the square root, square both sides of the equation:

   \[
   (\sqrt{5x})^2 = 10^2
   \]

   This simplifies to:

   \[
   5x = 100
   \]

3. **Solve for \( x \):** Divide both sides by 5 to isolate \( x \):

   \[
   x = \frac{100}{5}
   \]

   \[
   x = 20
   \]

So, the solution to the equation is:

\[
x = 20
\]

Would you like a detailed explanation on any part of this process, or have any questions?

Here are some related questions to deepen understanding:

1. What is the process for solving equations with other types of radicals, such as cube roots?
2. How can we verify if the solution to a radical equation is correct?
3. What are some common mistakes when solving radical equations?
4. How would the solution change if there was an additional constant inside the square root, like \(\sqrt{5x + 4} = 10\)?
5. How does this approach apply to equations with multiple radicals?

**Tip:** When solving radical equations, always check the solution by substituting it back into the original equation, as squaring both sides can sometimes introduce extraneous solutions.

Solve the equation involving radical expressions: √(5x) = 10.

Learn how to solve radical equations, such as √(5x) = 10, by isolating and squaring both sides. This algebra problem introduces key concepts in radical expressions and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation