Simplify the product. $$ \sqrt{3} \cdot \sqrt{12} $$

Question

UpStudy AI · Accepted Answer

To simplify the product $$\sqrt{3} \cdot \sqrt{12}$$, you can use the property of square roots that states:

$$
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \times b}
$$

Let's apply this property step by step:

1. **Multiply the radicands (the numbers inside the square roots):**

$$
\sqrt{3} \cdot \sqrt{12} = \sqrt{3 \times 12}
$$

2. **Calculate the product inside the square root:**

$$
3 \times 12 = 36
$$

So,

$$
\sqrt{3 \times 12} = \sqrt{36}
$$

3. **Simplify the square root:**

$$
\sqrt{36} = 6
$$

**Therefore,**

$$
\sqrt{3} \cdot \sqrt{12} = 6
$$
The product simplifies to 6.

Simplify the product. \[ \sqrt{3} \cdot \sqrt{12} \]