To simplify the expression √24 + 3√45 – 2√20, we start by simplifying each square root term individually.
1. **Simplifying √24:**
√24 can be broken down into √(4 × 6), which further simplifies to √4 × √6. Since √4 = 2, we have:
√24 = 2√6
2. **Simplifying √45:**
√45 can be expressed as √(9 × 5), which simplifies to √9 × √5. Since √9 = 3, we find:
√45 = 3√5
Now, substituting back, we get:
3√45 = 3 × 3√5 = 9√5
3. **Simplifying √20:**
√20 can be rewritten as √(4 × 5), simplifying to √4 × √5. Since √4 = 2, we have:
√20 = 2√5
Substituting back, we find:
2√20 = 2 × 2√5 = 4√5
Now we can substitute the simplified terms back into the original expression:
√24 + 3√45 – 2√20 = 2√6 + 9√5 – 4√5
4√5 and 9√5 can be combined since they have the same radical:
9√5 – 4√5 = 5√5
So, our expression becomes:
2√6 + 5√5
Thus, the simplified expression for √24 + 3√45 – 2√20 is:
2√6 + 5√5