How do you simplify √20 * √45 * √5?

To simplify the expression √20 * √45 * √5, we can start by multiplying the square roots together. The rule of multiplying square roots states that √a * √b = √(a * b).

Let’s break it down step by step:

1. First, we multiply the numbers inside the square roots:
   √20 * √45 * √5 = √(20 * 45 * 5).
2. Now, calculate the product: 20 * 45 = 900, and then 900 * 5 = 4500. Thus, we have:
   √(20 * 45 * 5) = √4500.

Next, we simplify √4500. We can factor 4500 into its prime factors:

• 4500 = 45 * 100 = 9 * 5 * 10 * 10 = 3^2 * 5^1 * (2^2 * 5^2) = 3^2 * 2^2 * 5^3.

Now, we can simplify by taking out the square roots of the perfect squares:

• √(4500) = √(3^2 * 2^2 * 5^3) = 3 * 2 * 5 * √5 = 30√5.

So, the simplified form of √20 * √45 * √5 is 30√5.