To simplify the expression 92√3 into its simplest radical form, we need to break down the number 92 and see if it has any perfect square factors.
The prime factorization of 92 can be expressed as:
- 92 = 4 × 23
Here, 4 is a perfect square since √4 = 2.
Now, we can rewrite 92√3 as:
- 92√3 = (4 × 23)√3 = 2√4 × 23√3
Using the property of square roots, we can take 2 out of the radical:
- = 2√(4) × √3 = 2√(92 × 3)
Thus, we can express it as:
- 92√3 = 2√(4 × 23 × 3) = 2√276
Since 276 does not simplify further (as it has no perfect square factors), we can conclude that the value that remains under the radical in its simplest form is:
- 276
Therefore, the answer to your question is that the value that remains under the radical when 92√3 is written in its simplest radical form is 276.