To simplify the expression \( 216\sqrt{32713} \), we first need to understand the components of the expression.
Let's write out \( 216 \) in terms of its prime factorization:
\[ 216 = 6^3 = (2 \cdot 3)^3 = 2^3 \cdot 3^3 \]
Now let's analyze \( \sqrt{32713} \). Since \( 32713 \) doesn't seem to have factors that are easily recognizable, we can assume \( \sqrt{32713} \) is in its simplest form. Therefore, we cannot simplify this radical further without knowing if \( 32713 \) has any square factors.
Given the problem asks for an expression that is equivalent to \( 216\sqrt{32713} \), we can keep \( 216 \) as \( 6^3 \) but won't adjust \( \sqrt{32713} \) since it is already in its simplest form.
Now we can write the complete expression as:
\[ 216\sqrt{32713} = 6^3\sqrt{32713} \]
Without any potential simplifications for \( \sqrt{32713} \), the expression remains as:
\[ 6^3 \cdot \sqrt{32713} \]
Next, we can evaluate each option provided:
- 8: This number does not relate to our expressions.
- 18: This is also not a simplification of the expression.
- 12: Like the previous choices, 12 is not a related simplification.
- Fraction \( \frac{1}{2} \): This does not match our expression.
- 2: Also does not match our expression.
None of the options provided correspond to the simplification of \( 216\sqrt{32713} \) directly.
Therefore, it seems like either the expression has a misunderstanding or none of the given options are corresponding correctly. If you have a specific simplification in mind or wish to clarify further, please provide more context, and I will be glad to assist you!
3 answers