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With a negative radicand (expression with a radical), this expression is going to be an imaginary number. And with imaginary numbers we use i to factor out the factor of -1:
Next, a simplified radical expression has ...
- No radicals in a denominator
- No fractions in a radicand
We have a fraction in the radicand so we have more work to do. Although there are other ways to simplify radicands with fractions, I like to start by making the denominator a perfect square. So we'll start by figuring out what we can multiply 125 by to turn it into a perfect square. Surely multiplying by 125 will work. But there is a smaller number that will work. And since smaller numbers are easier to work with, I prefer to go that way. Since I can see that just another factor of 5 will make 125 a perfect square, It will be the perfect square of 5*5 or 25:
Now we'll split the fraction into spearate square roots:
and replace with 25:
This is our simplified expression. An alternate form, which may be preferred by your teacher, would be:
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