Take a factor out of the square root:
a) √(10y²), where y<0
b) √(3y²), where y<0

a) y√10

b) y√3

Step-by-step explanation:

The opposite of square root is squaring a number. Opposite cancel each other out:

If you can't cancel everything out, you would leave the other numbers inside the root:

a)

√(10y²)

= √10 √y²        Apply the root to each number

= y√10          √y² cancelled out to y

Since 10 had no "double" factors, it can't be further simplified.

To find "double" factors, find prime factors of 10:

10 = 5 X 2

There are no repeated factors, so you leave 10 under the root.

b)

√(3y²)

= √3 √y²        Apply the root to each number

= y√3           √y² cancelled out to y

3 also does not have "double" factors.

3 = 3 X 1

Neither 3 nor 1 are square numbers.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2