Let's simplify each term first:

1. \( 8\sqrt{8} \):  
   Break down \( \sqrt{8} \) as follows:  
   \[
   \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}
   \]  
   Now, substitute back into \( 8\sqrt{8} \):  
   \[
   8\sqrt{8} = 8 \times 2\sqrt{2} = 16\sqrt{2}
   \]

2. \( 3\sqrt{2} \):  
   This term is already simplified.

3. \( 3\sqrt{12} \):  
   Break down \( \sqrt{12} \) as follows:  
   \[
   \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}
   \]  
   Now, substitute back into \( 3\sqrt{12} \):  
   \[
   3\sqrt{12} = 3 \times 2\sqrt{3} = 6\sqrt{3}
   \]

Now, putting it all together:
\[
8\sqrt{8} + 3\sqrt{2} + 3\sqrt{12} = 16\sqrt{2} + 3\sqrt{2} + 6\sqrt{3}
\]

Combine like terms:
\[
(16\sqrt{2} + 3\sqrt{2}) + 6\sqrt{3} = 19\sqrt{2} + 6\sqrt{3}
\]

Thus, the simplified expression is:
\[
19\sqrt{2} + 6\sqrt{3}
\]

Would you like more details on the simplification process or another explanation?

Here are 5 related questions:
1. How would you simplify \( 5\sqrt{18} + 2\sqrt{8} \)?
2. What is \( \sqrt{50} + \sqrt{2} \)?
3. How do you factor and simplify \( \sqrt{72} \)?
4. What is the result of combining \( 7\sqrt{3} + 2\sqrt{12} \)?
5. How do you simplify \( 4\sqrt{32} + 5\sqrt{2} \)?

**Tip:** Always look for perfect squares within the square root to simplify expressions efficiently!

Discover how to simplify the expression 8√8 + 3√2 + 3√12 by breaking down square roots and combining like terms. This solution walks through simplifying radicals, using properties of square roots, and is suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation