Question

Rewrite the irrational cube root root(189, 3) as the product of an integer and another irrational cube root. Show your work. Note: You will find the option to add a cubic root symbol in the Algebra (x) keyboard.
show the work short answer

Answer 1

easy

Answer 2

make it easier

Answer 3

To rewrite \( \sqrt[3]{189} \) as the product of an integer and another irrational cube root, we first factor \( 189 \).

1. Factor \( 189 \):
- \( 189 = 3 \times 63 \)
- \( 63 = 3 \times 21 \)
- \( 21 = 3 \times 7 \)
- Thus, \( 189 = 3^3 \times 7 \).

2. Now we can express the cube root:
\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7}.
\]

3. Using the property of cube roots, we can separate it:
\[
\sqrt[3]{189} = \sqrt[3]{3^3} \times \sqrt[3]{7}.
\]

4. Since \( \sqrt[3]{3^3} = 3 \), we now have:
\[
\sqrt[3]{189} = 3 \times \sqrt[3]{7}.
\]

Thus, the final answer is:
\[
\sqrt[3]{189} = 3 \times \sqrt[3]{7}.
\]

Answer 4

Glad you found it easy! If you have any more questions or need further assistance, feel free to ask!

Answer 5

Sure! Here’s a simplified way to explain the steps for rewriting \( \sqrt[3]{189} \):

1. **Factor 189:**
\( 189 = 3 \times 63 \)
\( 63 = 3 \times 21 \)
\( 21 = 3 \times 7 \)
So, \( 189 = 3^3 \times 7 \).

2. **Rewrite the cube root:**
\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7}
\]

3. **Split the cube root:**
\[
\sqrt[3]{189} = \sqrt[3]{3^3} \times \sqrt[3]{7}
\]

4. **Simplify:**
Since \( \sqrt[3]{3^3} = 3 \), you get:
\[
\sqrt[3]{189} = 3 \times \sqrt[3]{7}
\]

**Final Answer:**
\[
\sqrt[3]{189} = 3 \times \sqrt[3]{7}
\]

This keeps it straightforward and easy to understand! Let me know if you’d like more help!