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

Answer 1

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

The prime factorization of 189 is: \[ 189 = 3^3 \times 7 \]

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

Using the property of cube roots, we can separate this into two parts: \[ \sqrt[3]{189} = \sqrt[3]{3^3} \times \sqrt[3]{7} \]

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

Thus, we can rewrite \(\sqrt[3]{189}\) as: \[ \sqrt[3]{189} = 3\sqrt[3]{7} \]

Answer 2

Paragraph form

Answer 3

To rewrite the irrational cube root \(\sqrt[3]{189}\) as the product of an integer and another irrational cube root, we begin with the prime factorization of 189, which is \(189 = 3^3 \times 7\). This allows us to express the cube root as \(\sqrt[3]{189} = \sqrt[3]{3^3 \times 7}\). By applying the property of cube roots that allows us to separate products, we can write this as \(\sqrt[3]{3^3} \times \sqrt[3]{7}\). Since \(\sqrt[3]{3^3}\) simplifies to 3, we find that \(\sqrt[3]{189} = 3 \times \sqrt[3]{7}\). Thus, we can conclude that \(\sqrt[3]{189}\) can be rewritten as \(3\sqrt[3]{7}\).

Answer 4

Replace the symbols the numbers

Answer 5

To rewrite the irrational cube root of one hundred eighty-nine as the product of an integer and another irrational cube root, we begin with the prime factorization of one hundred eighty-nine, which is one hundred eighty-nine equals three cubed times seven. This allows us to express the cube root as the cube root of one hundred eighty-nine equals the cube root of three cubed times seven. By applying the property of cube roots that allows us to separate products, we can write this as the cube root of three cubed multiplied by the cube root of seven. Since the cube root of three cubed simplifies to three, we find that the cube root of one hundred eighty-nine equals three times the cube root of seven. Thus, we can conclude that the cube root of one hundred eighty-nine can be rewritten as three times the cube root of seven.

Answer 6

Write them as numbers not in word form

Answer 7

To rewrite the irrational cube root of 189 as the product of an integer and another irrational cube root, we begin with the prime factorization of 189, which is \(189 = 3^3 \times 7\). This allows us to express the cube root as \(\sqrt[3]{189} = \sqrt[3]{3^3 \times 7}\). By applying the property of cube roots that allows us to separate products, we can write this as \(\sqrt[3]{3^3} \times \sqrt[3]{7}\). Since \(\sqrt[3]{3^3}\) simplifies to 3, we find that \(\sqrt[3]{189} = 3 \times \sqrt[3]{7}\). Thus, we can conclude that \(\sqrt[3]{189}\) can be rewritten as \(3\sqrt[3]{7}\).

Answer 8

Write that in 7th grader words now

Answer 9

To rewrite the cube root of 189 as a product of a whole number and another cube root, we start by breaking down 189 into its prime factors. We find that 189 can be written as \(3^3 \times 7\). This means we can express the cube root like this: \(\sqrt[3]{189} = \sqrt[3]{3^3 \times 7}\).

Next, we use a property of cube roots that allows us to separate the pieces. This gives us \(\sqrt[3]{3^3} \times \sqrt[3]{7}\). Since the cube root of \(3^3\) is simply 3, we can simplify it to get \(3 \times \sqrt[3]{7}\).

So, we conclude that the cube root of 189 can be rewritten as \(3\sqrt[3]{7}\).

Answer 10

Write that in much simper form using letters, not symbols

Answer 11

To rewrite the cube root of 189 as a whole number times another cube root, we can start by factoring 189. We find that 189 equals 3 times 3 times 3 times 7, or three cubed times seven.

Now, we can say that the cube root of 189 is the same as the cube root of three cubed times seven.

Using a rule about cube roots, we can separate this into two parts: the cube root of three cubed and the cube root of seven. The cube root of three cubed is just 3.

So, we can rewrite the cube root of 189 as 3 times the cube root of 7.