Square root 5 (m+2) ^3

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)