Explain why each radical expression is or is not in simplified form.

1. 3/√3
It's not in simp form: √3

2. 5√30
It is in simp form

Okay, I know the answers... but what do they mean about "explain"? What do they want? Just the answer and how I got it or... ? If so, can someone help? Thanks

#1.

It's not in simplified form because there's a radical sign in the denominator.
to remove the radical sign, we multiply both numerator and denominator by √3:
(3 / √3) * (√3 / √3)
= 3√3 / 3
= √3

#2.
Yeah, it's already in simplified form.

Thank you!:)

When a question asks you to "explain," it typically means to provide a clear and thorough explanation of your answer or reasoning. For example, if a radical expression is not in simplified form, you can explain why by pointing out any potential simplifications that could be done and why it has not been done in that particular expression.

In the case of 3/√3, the expression is not in simplified form because the denominator contains a radical (√3). To simplify this expression, you could rationalize the denominator by multiplying both the numerator and denominator by √3. This would result in 3√3/√3√3, which simplifies to 3√3/3. Further simplification yields √3.

On the other hand, for an expression like 5√30, if it is already simplified, you can explain that there are no perfect-square factors remaining within the radical. In this case, 30 can be factored into 2 * 3 * 5, so the expression can be rewritten as 5 * √(2 * 3 * 5). However, none of these factors are perfect squares, so the expression cannot be simplified further.

When someone asks you to explain why a radical expression is or is not in simplified form, they want you to provide a justification for your answer. Simply providing the answer and how you arrived at it is not enough; you need to provide a clear explanation of what it means for a radical expression to be simplified or not.

In the first example, the expression is 3/√3. To determine if it is in simplified form, we need to check if there are any common factors between the numerator (3) and the denominator (√3). Since √3 cannot be simplified further, we can say that 3/√3 is not in simplified form because the denominator contains a radical (√3). The answer explains that the presence of the radical makes the expression not simplified.

In the second example, the expression is 5√30. To determine if it is in simplified form, we need to check if the radical (√30) can be simplified further. To do that, we can break down 30 into its prime factors: 30 = 2 * 3 * 5. We can see that the square root of 30 can be simplified as the square root of 2 * 3 * 5, which equals the square root of 2 times the square root of 3 times the square root of 5. Since none of these factors can be further simplified, we can say that 5√30 is in simplified form. The answer explains that the absence of any further simplifications means that the expression is already in its simplest form.

By providing these explanations, you are helping the person understand not only the answer but also the reasoning behind it.