Simplify the product.
-9 sqrt 28a^2 * 1/3 sqrt 63a
I came until -3 sqrt 49a^2 * sqrt 36a, but then I got confused...
-9 √(28a^2) * 1/3 √(63a)
-9 * (2a√7) * 1/3 (3√(7a))
-6a √(49a)
-42a√a
The answer key says -126√a.
My bad. You are correct.
I dropped a 3 after the 2nd line.
But then, you caught that when you checked my math.
Right?
To simplify the given product step-by-step, we can follow these steps:
1. Starting with the original expression: -9 √(28a^2) * (1/3) √(63a)
2. Simplify the square roots separately:
√(28a^2) can be written as √(4*7*a*a), which simplifies to 2a√7.
√(63a) can be written as √(9*7a), which simplifies to 3√7a.
3. Substitute the simplified square roots back into the expression:
-9 * 2a√7 * (1/3) * 3√7a
4. Simplify the coefficients:
-9 * 2 * 1 * 3 = -54
5. Simplify the variables:
√7 * √7 = 7
a * a = a^2
Now, we can put everything together:
Final simplified expression: -54a^2 * 7
= -378a^2