Let's take a closer look at some of the specifics that relate to working with radicals.

The notation:
radicalparats
The radical symbol is infosymbol.
In 1525, the radical symbol first appeared in print as simply the infosmallradportion. The horizontal segment bar over the numbers inside the radical (called a vinculum) did not appear. In 1637, mathematician Rene Descartes added the vinculum, thus creating the radical symbol that is used today.

 The radical symbol may also be referred to as a "radical sign", a "root symbol", or a "surd".


So, what is a "surd"?

The term "surd" refers to a number left in radical form for accuracy, which when written in decimal form would go on forever without repeating. The number under the root symbol is a rational number and is not a perfect square. Surds are roots that are irrational numbers.

Surds which have a root index of two are quadratic surds.
Surds which have a root index of three are cubic surds.
Surds which have a root index of four are fourth order surds.
And so on ...

inforsurds22

Is the "index" odd or even?
radicalparats
When the radical symbol is used without an "index" indicated, it is implied to be the "square root" of a value. Otherwise, the type of "root" is determined by the appearance of the "index" value.

repic1

If the index is an odd number, the radicand can be a negative value.
Raising a negative real number to an odd power will result in a negative value.
(-2)(-2)(-2)(-2)(-2) = -32

If the index is an even number, the radicand can not be a negative value.
It is not possible to raise a negative real number to an even power and get a negative value.
repic2

(Note: Our work in this unit is dealing with real numbers, not complex numbers.)

 
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