Question

The order of the surd 6 √2187 after simplification is​

Answer 1

`n = 162`

Explanation:

Given

`6\sqrt{2187`

Required

Determine the order of the surd

If a surd is represented as
`n\sqrt{r`, then the order of the surd is
`n`

`6\sqrt{2187`

Express 2187 as
`3^6 * 3`

`6√(2187) = 6√(3^6 * 3)`

Split the surd

`6√(2187) = 6√(3^6) * √(3)`

Apply the following law of indices:

`√(a) = a^{(1)/(2)}`

The expression becomes:

`6√(2187) = 6 * 3^{(6)/(2)} * √(3)`

`6√(2187) = 6 * 3^(3) * √(3)`

`6√(2187) = 6 * 27 * √(3)`

`6√(2187) = 162 * √(3)`

`6√(2187) = 162 √(3)`

By comparing
`162 √(3)` to
`n\sqrt{r`, we can say that:

`n = 162`

`r = 3`

Conclusively, the order of the surd is 162