MATH 096 §7.1 Radicals and Radical Functions
Objective
1.
Find Square Roots
2.
Find Cube Roots
3.
Find the 𝑛th roots. 𝑛
4.
Find √𝑎 𝑛 where 𝑎 is a real number
5.
Graph Square and Cube Root Functions
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Recall

A square root of a number 𝑎 is a number whose square is 𝑎.
Ex. 5 and − 5 are square roots of 25
 Denote the nonnegative (or principal) square root with the radical sign
Ex. √25 = 5
 Denote the negative square root with the negative radical sign
Ex. −√25 = −5
 Radical expression : √𝑎
Example Simplify. Assume that all variables represent positive numbers.
Example Find the cube roots.
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Example Simplify the following expressions.
Recall that √𝑎 2 is the positive square root of 𝑎 2 .
Ex. √(−7) 2 = √49 = 7
When variables are present in the radicand it is unclear whether the variable represents a positive or a negative number, absolute value bars are needed to ensure that the result is a positive number. Ex. √𝑥 2 = |𝑥|
Example Simplify.
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Definition Radical functions are functions of the form 𝒏 𝒇(𝒙) = √𝒙
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Example If 𝑓(𝑥) = √𝑥 − 4 and 𝑔(𝑥) = √𝑥 + 2 , find each function value.
Example Graph the square root function 𝑓(𝑥) = √𝑥
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