Section 7.1
Radicals and Radical Functions
Objectives:
• Find square roots
• Approximate roots.
• Find cube roots
• Find nth roots
• Find
where a is a real number
• Graph square and cube root functions
Finding Square Roots:
Principal Square Root:
Negative Square Root:
Radical sign:
Radicand:
Finding Square Roots:
Find each square root. Assume that all variables represent
nonnegative real numbers.
Perfect Squares and Cubes:
Perfect Squares through
Perfect Cubes through
Approximating Square Roots:
Irrational Numbers:
Find the approximate value of:
Check:
Finding Cube Roots:
Square Roots:
Cube roots:
Cube Root
The cube root of a real number a is written as:
if
Try this with 4 and ‐4.
Finding Cube Roots:
Find each cube root.
Finding nth roots:
Power:
Index:
How would I undo raising a number to the 17th power?
Finding nth roots:
Find each root. Identify the index.
Odd and even roots and negative numbers:
Powers of 2 and 3:
Finding
:
Simplify. Assume the variables represent any real number.
If n is an even positive integer, then:
If n is an odd positive integer, then:
Radical Functions:
If
Graph
and
find: