To simplify the expression √20 × √45 × √5, we can start by breaking down each square root into its prime factors.
1. **Breaking down the square roots:**
- √20 = √(4 × 5) = √4 × √5 = 2√5
- √45 = √(9 × 5) = √9 × √5 = 3√5
- √5 remains the same as it is already simplified.
2. **Replacing the original square roots:**
Now, substituting back, we have:
√20 × √45 × √5 = (2√5) × (3√5) × √5
3. **Combining the terms:**
We can now combine the coefficients (the numbers in front) and the square roots:
(2 × 3) × (√5 × √5 × √5) = 6 × (√5 × √5 × √5)
4. **Simplifying further:**
We know that √5 × √5 = 5, so:
6 × (√5 × 5) = 6 × 5 × √5 = 30√5
5. **Final result:**
Thus, the simplified form of the expression √20 × √45 × √5 is 30√5.