Roots and Irrational Numbers Unit Test

Question

Math 8 Q2 (Pre-Algebra) / Roots and Irrational Numbers

rewrite the irrational cube root ∛189 as a product of an integer and another irrational cube root. show your work

Answer 1

To rewrite the irrational cube root ∛189 as a product of an integer and another irrational cube root, we need to find a perfect cube factor of 189.

The prime factorization of 189 is:
189 = 3 × 3 × 3 × 7

Let's break it down into perfect cubes:
189 = (3 × 3 × 3) × 7 = 27 × 7

Now, rewrite the irrational cube root ∛189:
∛189 = ∛(27 × 7)

Since 27 is a perfect cube, we can rewrite it as:
∛189 = ∛(27 × 7) = ∛27 × ∛7

The cube root of 27 is 3, so we have:
∛27 = 3

Therefore, we can rewrite the irrational cube root ∛189 as a product of an integer and another irrational cube root:
∛189 = 3∛7

Answer 2

put it in first person pov when your talking about solving it and put it in complete sentences

Answer 3

To rewrite the irrational cube root ∛189 as a product of an integer and another irrational cube root, I need to find a perfect cube factor of 189. First, I'll find the prime factorization of 189, which is 3 × 3 × 3 × 7. Breaking it down further, I can see that 189 equals 27 × 7.

Now, I can rewrite the irrational cube root ∛189 as ∛(27 × 7). Since 27 is a perfect cube, I can simplify it as the cube root of 27, which is 3. Therefore, the irrational cube root ∛189 can be written as 3 (∛7).