Question

Write problem as a single radical using the smallest possible root. 16

Answer 1

The radical expression is given to be:

`√(n^5)\sqrt[3]{n^4}`

Recall the rule:

`\sqrt[n]{x}=x^{(1)/(n)}`

Therefore, the expression becomes:

`√(n^5)\sqrt[3]{n^4}=n^{(5)/(2)}\cdot n^{(4)/(3)}`

Recall the rule:

`x^a\cdot x^b=x^(a+b)`

Therefore, we have:

`n^5\cdot n^{(4)/(3)}=n^{(5)/(2)+(4)/(3)}`

Since:

`(5)/(2)+(4)/(3)=(23)/(6)`

Therefore, the expression becomes:

`n^{(5)/(2)+(4)/(3)}=n^{(23)/(6)}`

Therefore, we can rewrite the radical to be:

`\Rightarrow\sqrt[6]{n^(23)}`