https://file.aiquickdraw.com/mathbot/file/17279259564380x7c45gp.jpg

The expression shown in the image is:

\[
3 \sqrt{3} \left( 4 \sqrt{3} + 3 \right)
\]

Let's simplify this step by step.

### Step 1: Distribute \(3 \sqrt{3}\) to both terms inside the parentheses.
\[
3 \sqrt{3} \times 4 \sqrt{3} + 3 \sqrt{3} \times 3
\]

### Step 2: Multiply the first part: \(3 \sqrt{3} \times 4 \sqrt{3}\).
\[
3 \times 4 \times \sqrt{3} \times \sqrt{3} = 12 \times 3 = 36
\]

### Step 3: Multiply the second part: \(3 \sqrt{3} \times 3\).
\[
3 \times 3 \times \sqrt{3} = 9 \sqrt{3}
\]

### Step 4: Combine the results.
\[
36 + 9 \sqrt{3}
\]

Thus, the simplified expression is:

\[
36 + 9 \sqrt{3}
\]

Let me know if you'd like more details or further explanation.

Here are 5 related questions to expand on this:

1. What is the general rule for multiplying square roots with coefficients?
2. Can you factor out any terms from \(36 + 9 \sqrt{3}\)?
3. How would you approach simplifying an expression with higher powers of square roots?
4. What happens if you had a different base under the square root, like \(\sqrt{5}\) instead of \(\sqrt{3}\)?
5. How would you solve the equation if this expression were equal to a value, like \(36 + 9 \sqrt{3} = x\)?

**Tip:** When simplifying expressions with square roots, always combine like terms and apply basic properties of square roots such as \(\sqrt{a} \times \sqrt{a} = a\).

Simplify the expression 3√3(4√3 + 3).

Simplify the expression 3√3(4√3 + 3) using multiplication of square roots and the distributive property. Follow step-by-step instructions for distributing and combining like terms to arrive at the simplified expression 36 + 9√3. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation