Question

Cna someone explain me what is a radical expression? what is the index of a radical?

Answer 1

A radical expression is any root of a number:
\[\sqrt[2]{3}\]
\[\sqrt[5]{25}\]
or the most basic
\[\sqrt{3}\]
The index is the root you are taking, in my examples 2, 5, and 2

Answer 2

A radical is an expression with a square root, cube root etc.
\[\sqrt{x + 3}\]
This is an example of radical.

Answer 3

can the radicand be negative when the index is odd?

Answer 4

yes, in fact the radical can be negative with an even index as long as you can have imaginary numbers. with an odd index you will have a real solution with a negative radical

Answer 5

Thank you so much for your help. Can you give me an example of a radical expression but not with a perfect root.

Answer 6

√2 is a radical expression that's not a perfect root. The index is 2 (as any radical without the index labeled is always assumed to be 2). It's generally read as "the square root of 2." The answer is an irrational number around 1.41421356

Answer 7

Can you show me one that has to be simplified using factoring?

Answer 8

If you look at √45 then you can rewrite 45 as 9*5 (you want to factor out the largest perfect square that goes into 45, in this case 9) and you have √(9*5), next you break up the square root into two pieces √9*√5 and then solve: 3√5

Answer 9

Oh Gosh, I just got my brain melt with this one. LOL

Answer 10

Is that what you meant by simplifying by factoring? Or where you thinking about something different?

Answer 11

I'm just learning with you right now. Go slow with me LOL. I'm trying to understand my lesson for this week and for me this is another language.

Answer 12

That's alright. If we look at √112 and try to simplify

Answer 13

First we look at perfect squares (4, 9, 16, 25, 36, 49, etc)
Which one of these divide into 112?

Answer 14

If break it down in parts I'm sure I will get it

Answer 15

I think 4, 16, 36

Answer 16

112/36 = 3.11111111
112/16 = 7
112/4 = 28
So the largest perfect square that goes into 112 is 16

Answer 17

rewriting 112 as a product (factored form) yields 16*7
so √112 = √(16*7)

Answer 18

and that's it?

Answer 19

Almost, If you break that into parts you have √16*√7, and what's that simplified?

Answer 20

\[4\sqrt{7}\]

Answer 21

Excellent. That's all there is to it. Break the number down into perfect roots and then simplify.

Answer 22

yeahhhhhh I got it...

Answer 23

Awesome thank You so much for all your help.