Question

Can I get some help with these math problems? Algebra 1B

Answer 1

1a. -5

1b. 3

1c. -5i

2. S = 11 m

3. S = 4 ft.

Explanation:

1a. ∵ cube root of -125 means ∛(-5)(-5)(-5) = ∛(-5)³

∴
`((-5)^(3))^{(1)/(3)}` = -5

1b.
`\sqrt[4]{81}=\sqrt[4]{(3)(3)(3)(3)} =\sqrt[4]{(3)^(4) }=(3^(4))^{(1)/(4)}=3`

1c.
`\sqrt[4]{-625}=\sqrt[4]{(-1)(625)}`

∵ i =
`\sqrt[4]{-1}`

∴
`\sqrt[4]{(-1)(625)}= i \sqrt[4]{5^(4)} =i (5^(4))^{(1)/(4) } = 5i`

2. The volume of the cube = S³

∵ V = 1331 m³

∴ S = ∛1331 = 11 m

3. The volume of the cube = S³

∵ V = 64 ft.³

∴ S = ∛64 = 4 ft.