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 of 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 3 x 3 x 3 x 7.

Since 189 has a perfect cube factor of 3 x 3 x 3, we can rewrite the cube root of 189 as:

∛189 = ∛(3 x 3 x 3 x 7)

Now we can simplify the cube root:

∛(3 x 3 x 3 x 7) = 3∛(3 x 7)

Therefore, the irrational cube root of 189 can be rewritten as:

∛189 = 3∛(3 x 7)

So, the product of an integer and another irrational cube root that represents ∛189 is 3∛(3 x 7).