Radicals…

Any expression using the form, 
is called a radical. N is the index (which is the number of times the radical needs to be multiplied by itself), x is the radicand, and if there is a number to be multiplied by the radical, it is called the coefficient.

We’ve learnt that Radicals go into two categories; entire radicals and mixed radicals;
Entire radicals are radicals where the whole expression is under the root symbol, whereas a mixed radical is when the radical is divided into a radical and coefficient.

How to change an entire radical with an index of two into a mixed radical…
An entire radical may be expressed as a mixed radical when the perfect square has been factored out of the entire radical. If you have the highest perfect square there will less steps than if you just factor out lower perfect squares. (And it is always expected that the answer will be in simplest form)

How to change a mixed radical of index 2 may be expressed an an entire radical by converting the number outside the radical symbol into a radical and then multiplying by the radicand… the number outside the radical symbol can be converted into a radical by raising it to the power of the index 2.

Example for turning an entire radical index 2, into a mixed radical…

 

 

 

 

 

 

 

 

 

 

 

 

 

Example for turning a mixed radical index 2, into an entire radical…