Question

Question #5caf9

Answer 1

Factor the rad a bit more....see below

Explanation:

`sqrt18 = sqrt(2 * 3 * 3) = 3 sqrt2`

Answer 2

`color(red)(sqrt450=15sqrt2`

Explanation:

`sqrt(450)=5sqrt18`

`:.sqrt(2*3*3*5*5)=5sqrt(2*3*3)`

`:.sqrt3*sqrt3=3` and`sqrt5*sqrt5=5`

`:.3*5sqrt2=3*5sqrt2`

`:.color(red)(sqrt450=15sqrt2`

Answer 3

The answer to your question: "Can there be multiple answers when simplifying radicals?" is no.

Explanation:

If you follow the information in the answers from both Barney and Eddie together you will see that the first radical you provided is not the complete simplification, and you must do one more step.

It is the same as `32/64=2/4`, which is correct, but not the complete solution to the question. The answer is `1/2` when simplified.

Answer 4

No.

Explanation:

Given radical can be presented in many forms

1. `sqrt450=5sqrt18`
2. `sqrt450=3sqrt50`
3. `sqrt450=15sqrt2`
4. `sqrt450=sqrt450`

As far as equivalence is concerned all four are equal.
However, the simplified radical, as per convention, is only appearing at number 3. The reason being

A. no perfect square factors other than `1` in the radicand
B. The denominator is always rationalized so that no radicals appear in the denominator of a fraction.