To simplify the expressions involving square roots, we’ll break them down step by step. Here’s how we can simplify each one:
1. Simplifying √24:
First, we can factor 24 into its prime factors:
- 24 = 4 × 6 = 2² × 2 × 3
Now, we can take the square root of the perfect square (4):
- √24 = √(4 × 6) = √4 × √6 = 2√6
2. Simplifying 3√45:
Next, we simplify 3√45. Similar to before, we’ll factor 45:
- 45 = 9 × 5 = 3² × 5
Now we take the square root of the perfect square (9):
- 3√45 = 3(√9 × √5) = 3(3√5) = 9√5
3. Simplifying 2√20:
Lastly, let’s simplify 2√20. We can factor 20 as follows:
- 20 = 4 × 5 = 2² × 5
Taking the square root of 4:
- 2√20 = 2(√4 × √5) = 2(2√5) = 4√5
Final Answers:
In summary, the simplified forms of the expressions are:
- √24 = 2√6
- 3√45 = 9√5
- 2√20 = 4√5
These simplified expressions are easier to work with and understand.