Exercise 117 Page &nbsp; 303

Split into factors

a=sqrt((- 4) * (- 4) * (- 4))

Write as a power

a=sqrt((- 4)^3)

sqrt(a^3)=a

a=- 4

The cube root of sqrt(- 64) is - 4.

b A fifth root is a number you can multiply by itself five times to get the value inside the radical.

a* a * a * a * a= a^5 = 32 In this case, we need the number that can be multiplied five times to get 32.

a=sqrt(32)

Split into factors

a=sqrt(2 * 2 * 2 * 2 * 2)

Write as a power

a=sqrt(2^5)

sqrt(a^5)=a

a=2

The fifth root of sqrt(32) is 2.

c A cube root is a number you can multiply by itself three times to get the value inside the radical.

a* a * a = a^3 = - 8 In this case, we need the number that can be multiplied three times to get - 8.

a=sqrt(- 8)

Split into factors

a=sqrt((- 2) * (- 2) * (- 2))

Write as a power

a=sqrt((- 2)^3)

sqrt(a^3)=a

a=- 2

The cube root of sqrt(- 8) is - 2.

d A fourth root is a number you can multiply by itself four times to get the value inside the radical.

a* a * a * a = a^4 = 10000 In this case, we need the number that can be multiplied four times to get 10000.

a=sqrt(10000)

Split into factors

a=sqrt(10 * 10 * 10 * 10)

Write as a power

a=sqrt(10^4)