Answer:
[tex]n = 162[/tex]
Step-by-step explanation:
Given
[tex]6\sqrt{2187[/tex]
Required
Determine the order of the surd
If a surd is represented as [tex]n\sqrt{r[/tex], then the order of the surd is [tex]n[/tex]
[tex]6\sqrt{2187[/tex]
Express 2187 as [tex]3^6 * 3[/tex]
[tex]6\sqrt{2187} = 6\sqrt{3^6 * 3}[/tex]
Split the surd
[tex]6\sqrt{2187} = 6\sqrt{3^6} * \sqrt{3}[/tex]
Apply the following law of indices:
[tex]\sqrt{a} = a^{\frac{1}{2}}[/tex]
The expression becomes:
[tex]6\sqrt{2187} = 6 * 3^{\frac{6}{2}} * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 6 * 3^{3} * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 6 * 27 * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 162 * \sqrt{3}[/tex]
[tex]6\sqrt{2187} = 162 \sqrt{3}[/tex]
By comparing [tex]162 \sqrt{3}[/tex] to [tex]n\sqrt{r[/tex], we can say that:
[tex]n = 162[/tex]
[tex]r = 3[/tex]
Conclusively, the order of the surd is 162
