Asked by bot gpt v 3.5

Rewrite the irrational cube 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 ( ×
) keyboard.

(2 points)
Answered by bot gpt v 3.5
can you put all in a sentence
Answered by bot gpt v 3.5
whats the answer
Answered by bot gpt v 3.5
can you rewrite it but with out the /)}[ all that just get rid of it
Answered by bot gpt v 3.5
with the sentence
Answered by bot gpt v 3.5
no im talking abt thisThe irrational cube root of 189 can be expressed as the product of an integer and another irrational cube root by rewriting it as \( \sqrt[3]{189} = 3 \times \sqrt[3]{7} \), following the prime factorization \( 189 = 3^3 \times 7 \). redo it with out the (/%
Answered by GPT-4o mini
To rewrite the cube root of 189 as the product of an integer and another irrational cube root, we can follow these steps:

1. **Prime Factorization of 189**:
First, we need to factor 189 into its prime components.

- 189 is odd, so it's not divisible by 2.
- The sum of the digits (1 + 8 + 9 = 18) is divisible by 3, so we can divide by 3:
\[
189 \div 3 = 63
\]
- Next, we factor 63, which is also divisible by 3:
\[
63 \div 3 = 21
\]
- Finally, we factor 21, which is also divisible by 3:
\[
21 \div 3 = 7
\]
- Thus, the complete prime factorization of 189 is:
\[
189 = 3^3 \times 7
\]

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

3. **Use the Property of Cubed Roots**:
We can separate the cube root using the multiplication property:
\[
\sqrt[3]{189} = \sqrt[3]{3^3} \times \sqrt[3]{7}
\]

4. **Simplify**:
We know that \(\sqrt[3]{3^3} = 3\). So we can rewrite the expression:
\[
\sqrt[3]{189} = 3 \times \sqrt[3]{7}
\]

Thus, the irrational cube root of 189 can be expressed as:
\[
\sqrt[3]{189} = 3 \times \sqrt[3]{7}
\]

This is your final answer, showing the composition of an integer and another irrational cube root.
Answered by GPT-4o mini
The irrational cube root of 189 can be expressed as the product of an integer and another irrational cube root by rewriting it as \( \sqrt[3]{189} = 3 \times \sqrt[3]{7} \), following the prime factorization \( 189 = 3^3 \times 7 \).
Answered by GPT-4o mini
The answer is:

\[
\sqrt[3]{189} = 3 \times \sqrt[3]{7}
\]
Answered by GPT-4o mini
Sure! The answer can be stated as:

The cube root of 189 is equal to 3 times the cube root of 7.
Answered by GPT-4o mini
The cube root of 189 can be expressed as 3 times the cube root of 7.
Answered by GPT-4o mini
Certainly! Here’s the revised sentence without any symbols:

The irrational cube root of 189 can be expressed as the product of an integer and another irrational cube root by rewriting it as the cube root of 189 equals 3 times the cube root of 7, following the prime factorization of 189 equals 3 cubed times 7.