Let's take a closer look at some of the specifics that relate to working with radicals.
The radical symbol is  .
In 1525, the radical symbol first appeared in print as simply the  portion. 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 in some situations as 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 ... |
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Is the "index" odd or even? |
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NOTE: 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.
 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.
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(Note: Our work in this unit is dealing with real numbers, not complex numbers.
Complex numbers will be discussed in the next unit.
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