Question

1. drag the correct simplification to each problem.

simplify.

1. $3\sqrt{5} \cdot 4\sqrt{2}$
2. $\sqrt{2} \cdot \sqrt{4}$
3. $4\sqrt{3} \cdot \sqrt{9}$
4. $\sqrt{15}(3 + \sqrt{3})$
5. $\sqrt{6}(3 + \sqrt{2})$

choices
$3\sqrt{15} + 3\sqrt{5}$
$12\sqrt{3}$
$2\sqrt{2}$
$12\sqrt{10}$
$3\sqrt{6} + 2\sqrt{3}$
$7\sqrt{7}$
$\sqrt{6} + \sqrt{2}$
$\sqrt{15} + \sqrt{2}$

Explanation:

Problem 1: \( 3\sqrt{5} \cdot 4\sqrt{2} \)

Step 1: Multiply the coefficients and the radicals separately.

The coefficient part: \( 3 \times 4 = 12 \)
The radical part: \( \sqrt{5} \times \sqrt{2}=\sqrt{5\times2}=\sqrt{10} \)

Step 2: Combine the results.

So \( 3\sqrt{5} \cdot 4\sqrt{2}=12\sqrt{10} \)

Step 1: Simplify \( \sqrt{4} \)

We know that \( \sqrt{4} = 2 \)

Step 2: Multiply with \( \sqrt{2} \)

\( \sqrt{2} \times 2 = 2\sqrt{2} \)

Step 1: Simplify \( \sqrt{9} \)

\( \sqrt{9}=3 \)

Step 2: Multiply the coefficients and the radical.

The coefficient part: \( 4\times3 = 12 \)
The radical part remains \( \sqrt{3} \)
So \( 4\sqrt{3} \cdot \sqrt{9}=12\sqrt{3} \)

Answer:

\( 12\sqrt{10} \)

Problem 2: \( \sqrt{2} \cdot \sqrt{4} \)