Algebra II
Radicals Introduction Show Me Notes
“Perfect” Values:
Name: _______________________
Date: ___________
Definition of a Perfect Square:
Perfect Squares to know:
Variable Perfect Square:
Definition of a Perfect Cube:
Perfect Cubes to know:
Variable Perfect Cube:
What would make something a perfect fourth?
Perfect fifth?
Radicals:
What does the symbol
mean?
What does the symbol:
3
mean:
Label the parts to this radical:
ca b
Create a radical with the following characteristics:
a) a square root with a radicand of 4 and a
b) a fifth root with a radicand of b and a
coefficient of -7
coefficient of y.
c) Why is
81  9 ?
d) Why is 3 125  5 ?
e) What is 3 49 ?
Remember:
…when your radicand is a ‘perfect’ number, when you simplify the radical goes away.
…your index tells you how many times you need a factor to repeat in the radicand in order to
simplify the radical
Non-perfect Radicands
20 This expression says ‘what number times
itself gives us 20’…. Umm, there isn’t one. So
how can we simplify it? We take any factors of
20 that multiply by itself. Let’s see what factors
give us 20 – break it down!
Simplifying Non-Perfect Radicands
1) Prime factor the radicand
2) Using the index, determine how many
repetitions of a factor we need.
3) Pull out the repeating factors as part of the
coefficient; leave the other factors as part of
the radicand.
Variables: the same rules apply, you need to
take out the repeating factors based on the
index. Any extra repeating factors stay as the
radicand.
Short cut: divide the exponent by
the index – quotient is the exponent of the
coefficient, the remainder is the exponent of
the radicand.
20
3
300x5
5 4 96a6b3
2 3 125c5 d 9 f 7
Your Turn – Try these three….
72
3
108x 4
63