Question

Take a factor out of the square root:
1. Square root of 10y^2, where y<0
2. Square root of x^3
3.Square root of a^5
4.Square root of 16y^7
5.Square root of 3x^3/16
Please answer all 10 points per question

Answer 1

Answer:

1.  |y| sqrt(10)

2.  |x| sqrt(x)

3. a^2 sqrt(a)

4.  4 |y|^3 sqrt(3)

5.  1/4 *|x| sqrt(3x)

Step-by-step explanation:

1.  sqrt(10y^2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(y^2) sqrt(10)

|y| sqrt(10)

We take the absolute  value of y because -y*-y = y^2 and the principle square root is y

2.  sqrt(x^3)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(x^2) sqrt(x)

|x| sqrt(x)

3. sqrt(a^5)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(a^4) sqrt(a)

a^2 sqrt(a)

4.  sqrt(16 y^7)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(16) sqrt(y^6)sqrt(y)

4 |y|^3 sqrt(3)

5.  sqrt(3/16x^3)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(1/16) sqrt(x^2)sqrt(3x)

1/4 *|x| sqrt(3x)