Question

Use the product property of radicals to simplify the following radical: √-81.

Answer 1

± 9i

Step-by-step explanation:

using the property of radicals

•
`√(ab)` =
`√(a)` ×
`√(b)`

•
`√(-1)` = i

given

`√(-81)`

=
`√(81(-1))`

=
`√(81)` ×
`√(-1)`

= ± 9i

Answer 2

To simplify the radical √-81 using the product property of radicals, we need to express -81 as the product of two numbers. The simplified form of the radical √-81 is -3i.

Step-by-step explanation:

To simplify the radical √-81 using the product property of radicals, we need to express -81 as the product of two numbers. Since -81 can be written as -9 * 9, we can simplify the radical as follows:

√-81 = √(-9 * 9) = √(-9) * √(9) = i * 3 = -3i

Therefore, the simplified form of the radical √-81 is -3i.