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When 92/3 is written in the simplest radical form, which value remains under the radical?
Solution:
Given, the value is 92/3
We find that 9 is raised to the power 2/3, which is a rational exponent.
We need to find the value that remains under the radical when 92/3 is written in the simplest radical form.
Using exponent property for radicals,
am/n = \(\sqrt[n]{x^{m}}\)
Given value can be written as
92/3= ∛92
92/3= ∛81
On further simplification,
92/3= ∛(3×3×3×3)
92/3= ∛(3³×3)
Now pulling out 3 from radical, we get
92/3= 3∛3
Therefore, the simplest form of expression will be 3∛3, and 3 will remain under radical.
When 92/3 is written in the simplest radical form, which value remains under the radical?
Summary:
The expression 92/3 written in the simplest radical form is 3∛3 and the value 3 remains under the radical.
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