How do you simplify the square root of 45?

To simplify the square root of 45, you can break it down into its prime factors. Here’s how you can do it:

Step-by-Step Simplification

First, factor 45 into its prime components:

• 45 = 9 × 5
• 9 can be further factored into 3 × 3

So, the complete factorization of 45 is:

• 45 = 3 × 3 × 5

Applying the Square Root

Now, you can take the square root:

• √45 = √(9 × 5)
• √45 = √9 × √5
• √9 = 3

Thus, you have:

• √45 = 3√5

Final Result

The simplified form of the square root of 45 is 3√5.