To simplify the expression 3 √20 + 2 √45, we first need to break down the square roots into their simplest forms.
Starting with √20:
- We can factor 20 as 4 × 5.
- Since 4 is a perfect square, we can simplify √20 as follows:
- √20 = √(4 × 5) = √4 × √5 = 2√5.
Now we have:
3 √20 = 3 × 2√5 = 6√5.
Next, let’s simplify √45:
- 45 can be factored as 9 × 5.
- Since 9 is a perfect square, we simplify √45 like this:
- √45 = √(9 × 5) = √9 × √5 = 3√5.
Now we have:
2 √45 = 2 × 3√5 = 6√5.
After simplification, we can rewrite the original expression:
3 √20 + 2 √45 = 6√5 + 6√5.
Finally, combine the like terms:
6√5 + 6√5 = 12√5.
So, the simplified form of 3 √20 + 2 √45 is 12√5.