Question

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

Answer 1

a) -y
`√(10\\)`

Explanation:

Answer 2

a) y√10

b) y√3

Explanation:

The opposite of square root is squaring a number. Opposite cancel each other out:
`\sqrt{x^(2)}=x`

If you can't cancel everything out, you would leave the other numbers inside the root:
`√(x^2y)=x√(y)`

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.