Question

√128ab^3
simplify square roots

Answer 1

`8b√(2ab)`

Explanation:

Rewrite 128a
`b^(3)` as
`(8b)^(2)` ⋅ (2ab).

Factor 64 out of 128.

`\sqrt{64 (2)ab^(3) }`

Rewrite 64 as
`8^(2)` .

`\sqrt{8^(2) . 2ab^(3)`

Factor out
`b^(2)`.

`\sqrt{8^(2) . 2a (b^(2)b)`

Move a.

`\sqrt{8^(2) . 2b^(2)ab`

Move 2.

`√(8^2b^2 . 2ab)`

Rewrite
`8^(2) b^(2)` as
`(8b)^(2)`.

`√((8b)^2 . 2 (ab))`

Add parentheses.

`√((8b)^2 . (2ab))`

Pull terms out from under the radical.

`8b√(2ab)`