Question

Which of the following will result in a rational answer?

What is the simplified form of the following expression?

7 (RootIndex 3 StartRoot 2 x EndRoot) minus 3 (RootIndex 3 StartRoot 16 x EndRoot) minus 3 (RootIndex 3 StartRoot 8 x EndRoot)

Answer 1

The simplified form of the given expression is
`7 (2x)^((1/3)) - 3 (16x)^((1/3)) - 3 (8x)^((1/3)).`

To simplify the given expression, we need to simplify each term separately and then combine them.

First, let's simplify the first term: 7 (RootIndex 3 StartRoot 2 x EndRoot)

The cube root of 2x is the same as raising 2x to the power of 1/3. So, we can rewrite it as
`(2x)^{(1/3).`.

Next, let's simplify the second term: 3 (RootIndex 3 StartRoot 16 x EndRoot)

The cube root of 16x is the same as raising 16x to the power of 1/3. So, we can rewrite it as
`(16x)^{(1/3).`

Finally, let's simplify the third term: 3 (RootIndex 3 StartRoot 8 x EndRoot)

The cube root of 8x is the same as raising 8x to the power of 1/3. So, we can rewrite it as
`(8x)^{(1/3).`

Now, let's substitute these simplified terms back into the original expression:

7 (RootIndex 3 StartRoot 2 x EndRoot) minus 3 (RootIndex 3 StartRoot 16 x EndRoot) minus 3 (RootIndex 3 StartRoot 8 x EndRoot)

=
`7 (2x)^((1/3)) - 3 (16x)^((1/3)) - 3 (8x)^((1/3)).`

Since each term involves taking the cube root of a variable raised to a power of 1/3, the answer will be rational. This is because taking the cube root of a number raised to a power of 1/3 results in a rational number.

Therefore, the simplified form of the given expression is
`7 (2x)^((1/3)) - 3 (16x)^((1/3)) - 3 (8x)^((1/3)).`