Question

which expression simplifies to 8√7. on top of the square root their is a little number and the little number is a 3

Answer 1

To determine which expression simplifies to \( 8\sqrt{7} \) with a cube root symbol (indicated by the little number 3), we need to consider that \( 8\sqrt{7} \) can be expressed in terms of cube roots.

The expression \( 8\sqrt{7} \) can be rewritten as follows:
- \( 8 \) is \( 2^3 \)
- \( \sqrt{7} \) is \( 7^{1/2} \)

Now, we can express \( 8\sqrt{7} \) entirely in terms of cube roots:
\[
8\sqrt{7} = 2^3 \cdot 7^{1/2} = (2^3) \cdot (7^{3/6}) = 2^3 \cdot 7^{1/2}
\]
Now to express \( 8\sqrt{7} \) under a single cube root, we note:
\[
8\sqrt{7} = \sqrt[3]{(2^3 \cdot 7^{3/6})^3}
\]
This implies:
\[
8\sqrt{7} = \sqrt[3]{(2^3 \cdot 7^{3/6})^3} = \sqrt[3]{(8)(7^{3/2})} = \sqrt[3]{\frac{8 \cdot 7^3}{7^{3/2}}}
\]

Thus, to represent \( 8\sqrt{7} \) in terms of a cube root, you could use:
\[
\sqrt[3]{512 \cdot 7^3}
\]
Where \( 512 = 8^3 \).

However, if the above simplifications do not match the restrictions of your question or if you're looking for a more straightforward expression involving cube roots specifically:

The expression you are looking for could be something like:
\[
\sqrt[3]{512 \cdot 7} \text{ or } \sqrt[3]{\frac{8 \cdot 7^{3/2}}{7^{1/2}}}
\]

If you have more context or specific expressions to check, it could help refine this into an exact response.

Answer 2

just answerr the question without any slashes or any /

Answer 3

The expression that simplifies to \( 8\sqrt{7} \) in terms of a cube root is:

**The cube root of 512 times 7.**

In mathematical notation, it would be written as:

**∛(512 * 7)**.