How do you simplify 9 square root 125?

To simplify the expression \(9 \sqrt{125}\), follow these steps:

Step 1: Break Down the Square Root

First, simplify the square root of 125. You can factor 125 into its prime factors:

• 125 = 25 × 5
• 25 is a perfect square (5 × 5)

Step 2: Simplify the Square Root

Now, rewrite the square root:

\(\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}\)

Step 3: Multiply by 9

Next, substitute back into the original expression:

Now, multiply:

\(9 \sqrt{125} = 9 \times 5\sqrt{5}\)

Final Result

So, the simplified form is:

45√5