Math Problem Statement

\sqrt{8}+3\sqrt{2}

Solution

The expression 8+32\sqrt{8} + 3\sqrt{2} can be simplified by expressing 8\sqrt{8} in terms of 2\sqrt{2}.

First, simplify 8\sqrt{8}:

8=4×2=4×2=22\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}

Now substitute this back into the original expression:

8+32=22+32\sqrt{8} + 3\sqrt{2} = 2\sqrt{2} + 3\sqrt{2}

Combine the like terms:

22+32=(2+3)2=522\sqrt{2} + 3\sqrt{2} = (2 + 3)\sqrt{2} = 5\sqrt{2}

So, the simplified expression is:

525\sqrt{2}

Would you like more details on this process or have any other questions?

Here are 5 related questions you might find interesting:

  1. How do you simplify the square root of a product?
  2. What is the process for adding or subtracting radical expressions?
  3. How do you simplify an expression like 50+22\sqrt{50} + 2\sqrt{2}?
  4. Can you combine radicals with different radicands (like 2+3\sqrt{2} + \sqrt{3})?
  5. How do you multiply and divide expressions involving square roots?

Tip: When simplifying square roots, always look for perfect squares within the radicand that can be factored out.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Square Roots
Radical Expressions
Combining Like Terms

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12