Math Problem Statement

6+6\sqrt{6+6}

Solution

We simplify the given expression:

6+6\sqrt{6+6}

Step 1: Add the terms inside the square root

6+6=126 + 6 = 12

Step 2: Simplify the square root

12\sqrt{12}

Step 3: Factorize 12 into perfect squares

12=4×3\sqrt{12} = \sqrt{4 \times 3}

Using the square root property:

4×3=23\sqrt{4} \times \sqrt{3} = 2\sqrt{3}

Final Answer:

23\mathbf{2\sqrt{3}}

Would you like a more detailed explanation? Let me know if you have any questions!

Here are five related questions to explore further:

  1. What is the square root of 18 simplified?
  2. How do you simplify 50\sqrt{50}?
  3. What is the exact value of 8+2\sqrt{8} + \sqrt{2}?
  4. How do you rationalize 15\frac{1}{\sqrt{5}}?
  5. What are the properties of square roots and radicals?

Tip: Always look for perfect square factors when simplifying square roots!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Square Roots
Simplification
Factoring

Formulas

√(a + b) = √a + √b (when terms are added inside a square root)

Theorems

Square root property

Suitable Grade Level

Grades 6-8