Radical Expressions

The " " symbol is called the radical symbol. When a number is added under the radical symbol, for instance, 16 , it becomes a radical expression. 16 can be read as "the square root of 16", "root 16" or "radical 16".

Each radical expression has an index and a radicand.

(radicand) (index)


The square root is the most popular radical. For instance 9 2 has a radicand of 9 and index of 2. However, it is written as 9 and the index of two is understood. "Squaring" a number and "taking the square root" are opposite operations.

3 2 =9so 9 =3

Numbers can be raised to powers other than two. For instance numbers can be cubed (raised to the 3rd power), and raised to the 4th, 5th , 6th and so on........ In the same way numbers can have different "roots".

Radical

Read as

Example

Opposite Operation

Square root

25 =5

52 = 25

Cube root

8 3 =2

23= 8

Fourth root

81 4 =3

34 = 81

nth root

Used to indicate "any" root

Not all radical expressions have a "perfect" number, for instance 5 . There is no number squared that will equal 5. Radical expressions can have an exact or an approximate answer. Exact answers will be left in radical form and approximate answers will be found with a calculator and will be a rounded decimal answer.

Radical expression

Simplified answer

Perfect/Non-Perfect

36

6 because 62 = 36

Perfect square

27 3

3 because 33 = 27

Perfect cube

7

7 answer in radical form

2.6 approximate answer

Non-Perfect

Radical expressions rely on a student having a strong multiplication background. Remember that "radical" and "root" mean the same thing. The index is the "root" and the number underneath is the radicand.

Related Links:
Math
algebra
Rationalizing a Binomial Denominator with Radicals
Simplifying radical expressions
Simplifying radical expressions with variables
Adding radical expressions
Simplifying Radicals Worksheets
Radical Form to Exponential Form Worksheets


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