# Lesson: Operations with Roots

## Comment on Operations with Roots

### For this problem:

For this problem:
a > 0
Quantity A: (4\sqrt{(5a)})^2
Quantity B: 40a

Quantity A:
[4√(5a)]² = [4√(5a)][4√(5a)]
= (16)(5a) ---> How do you get this? I would have thought 16 x sqrt(25a^2))
= 80a ### They're the same thing.

They're the same thing.

That is [4√(5a)]² = (16)[√(25a²)] = (16)[(√25)(√a²)] = (16)[(5)(a)] = 80a

### For the 2nd reinforcement

For the 2nd reinforcement activity I divided by 80a to get 1 and 1/2 instead of subtracting by 40a. Is there anything wrong with what I did? When we get to this point where we have...
QUANTITY A: 80a
QUANTITY B: 40a
...we could have just as easily divided both quantities by 80a (as you did) because we're told that a is positive.

When we do this, we get...
QUANTITY A: 1/2
QUANTITY B: 1
...in which case the answer is B.

Alternatively, we could have taken...
QUANTITY A: 80a
QUANTITY B: 40a
...and divided both quantities by 40a to get:
QUANTITY A: 2
QUANTITY B: 1