How would I know if a radical expression can be simplified? Can I always represent a radical expression in exponential form? Can you give an example?

Very simply radical expressions contain radical.

Now we have to find out what are radicals, and what is their implication.

Exponents are repeated multiplication:

a

^{m}= a. .a. .a.a,. (m times) , like 2^{4 }means 2 multiplied by intelf 4 times: 2

^{4}= 2 . 2 . 2. 2 = 16 Radicals are the opposite of the exponents, and are designated by √

^{----} Now if we ask what number has multiplied by itself 4 times to result in 16, then we write as :

4√16 = 2 , this read as 4th root of 16,

2nd root is referred to as square root, it is the relationship between side of a square and the area

3rd root is referred to as cube root, because corresponds the side of a cube and its volume.

2nd root or square root, the number 2 is not written.

√16 is read rad 16 or square root of 16

The general rule of definition of root is

^{n}√X^{ n}= X , on this ground we can represent roots equivalent of fractional exponent.

^{n}√X = X

^{1/n }

to find out the √16 = √(2. 2. 2. 2) = √2

^{4 }=(2^{4})^{1/2 }= 2^{2}= 4 These are square roots of perfect square numbers, √17 = 4.12

√16 = 4 √17= 4.12 √25 =5