Question

Please help!! (Click on the pic!)

Answer 1

`160√(3)`

Explanation:

Step 1: Know what the question is asking

• product ⇒ means to multiply

Step 2: Set up the problem

• 
  `(8√(8) )(5√(24) )`
• *Note: Multiplication is commutative ⇒ order doesn't matter, terms can be rearranged and the answer remains the same

1. 
   `8*√(8) *5*√(24)`
2. 
   `8*5*√(8) *√(24)`
3. 
   `40*√(8) *√(24)`

• *Note: It is easier to further simplify by simplifying the square roots before multiplying them together.

1. 
   `40*√(8) *√(24)`
2. 
   `40*√(4) *√(2) *√(4) *√(6)`
3. 
   `40*2*√(2) *2*√(6)`
4. 
   `40*2*2*√(2) *√(6)`
5. 
   `40*4*√(2) *√(6)`
6. 
   `80*√(12)`
7. 
   `80*√(4) *√(3)`
8. 
   `80*2*√(3)`
9. 
   `160√(3)`