Rewrite the irrational cube root 189−−−√3 as the product of an integer and another irrational cube root. Show your work.

Question

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(2 points)

Answer 1

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.

Answer 2

can you put all in a sentence

Answer 3

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 \( 189 = 3^3 \times 7 \).

Answer 4

whats the answer

Answer 5

The answer is:

\[ \sqrt[3]{189} = 3 \times \sqrt[3]{7} \]

Answer 6

can you rewrite it but with out the /)}[ all that just get rid of it

Answer 7

Sure! The answer can be stated as:

The cube root of 189 is equal to 3 times the cube root of 7.

Answer 8

with the sentence

Answer 9

The cube root of 189 can be expressed as 3 times the cube root of 7.

Answer 10

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 (/%

Answer 11

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.