To simplify the expression \( 3\sqrt{15} + \sqrt{21} - \sqrt{35} \), let's look at each term:

1. None of the square roots can be simplified further because none of the numbers inside the square roots (\(15\), \(21\), or \(35\)) are perfect squares or have a common factor that is a perfect square.
   
2. Since all of the square roots are in their simplest form, the terms cannot be combined directly because they involve different radicals.

Thus, the expression remains:

\[
3\sqrt{15} + \sqrt{21} - \sqrt{35}
\]

This is the simplified form.

Would you like more details on why these roots can't be simplified? 

Here are 5 questions related to this concept:

1. How do you simplify square roots involving perfect squares?
2. What does it mean for a square root to be in its simplest form?
3. How can you combine or add radical expressions?
4. What methods exist to estimate non-perfect square roots?
5. Can square roots with different radicands be factored in any way?

**Tip**: When simplifying square roots, always check if the number under the root has any perfect square factors.

Learn how to simplify the radical expression 3√15 + √21 - √35. This problem covers important concepts in radicals, including simplifying square roots and adding/subtracting radical expressions. 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