Square root of 24x^6y^9

Step-by-step explanation:

Break the expression into individual pieces

24 can be written as (4) (6)

x^6 can be written as (x^3) ^2

y^9 can be written as (y^4) ^2 (y)

Notice in the variables the focus on writing to the power of 2.

Square root and power of 2 are essentially inverse operations of each other, so they cancel each other out.

The square root of 4 is 2

The square root of (x^3) ^2 is x^3

The square root of (y^4) ^2 is y^4

The remaining 6 and y stay underneath the square root.

The final answer is then (2x^3y^4) (square root 6y)