Answer:
The square root of 5(m + 2)³ = (m + 2)√(5m + 10)
Step-by-step explanation:
* Lets think about how to change the root to the power
- We can change √x to x^(1/2)
# The number of the radical is the denominator of the fraction
and the power of the base under the radical is the numerator
of the fraction
- We can change √(x³) to x^(3/2)
* In our problem we have √[5(m + 2)³]
- Lets take the bracket (m + 2)³
# The bracket (m + 2)³ means (m + 2) × (m + 2) × (m + 2)
- So we can write it ⇒ (m + 2)²(m + 2)
* Now lets write the problem again with new factors
- √[5(m + 2)²(m + 2)]
∵ √(m + 2)² = [(m + 2)²]^1/2
- Multiply the power 2 by the power 1/2 and the answer is 1
∴ √(m + 2)² = (m + 2)
∴ √[5(m + 2)³] = (m + 2)√[5(m + 2)] = (m + 2)√(5m + 10)
* The square root of 5(m + 2)³ = (m + 2)√(5m + 10)
