Multiply. Write your answer in simplest form. $$ \sqrt{30} \cdot \sqrt{5} $$

Question

UpStudy AI · Accepted Answer

To multiply $$\sqrt{30}$$ and $$\sqrt{5}$$ and simplify the expression, follow these steps:

1. **Multiply the Square Roots:**

$$
   \sqrt{30} \cdot \sqrt{5} = \sqrt{30 \times 5} = \sqrt{150}
   $$

2. **Simplify $$\sqrt{150}$$:**

Break down 150 into its prime factors to find perfect squares:

$$
   150 = 25 \times 6
   $$

Here, 25 is a perfect square because $$25 = 5^2$$.

3. **Apply the Square Root to the Factors:**

$$
   \sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6}
   $$

So, the simplified form of $$\sqrt{30} \cdot \sqrt{5}$$ is:

$$
5\sqrt{6}
$$
$$5\sqrt{6}$$

Multiply. Write your answer in simplest form.