Transcript Simplifying Radicals

SIMPLIFYING RADICALS
High School Common Core
Number & Quantity
The Real Number System – Use properties of
rational and irrational numbers.

Means there is a note to read
at the bottom of the slide.
Simplifying Radicals
Radical
(also
called a
square
root)
A number
that, when
multiplied by
itself, will
give back that
number. You
“undo” an
exponent with
a radical.
x  x = x2 = x
3  3 =
9 =3
Index
The number
written outside
the radical
denoting its
inverse power.
2
49 =
3
27 =
3
33 = 3
16 =
4
24 = 2
4
72 = 7
Perfect
Squares
The numbers
that give you a
whole number
when you take
their square
root.
1
1
4
2
9
3
16
25
4
5
36
6
49
7
64
8
81
9
100
10
Determine
16 = 4
Determine
81 = 9

Determine
121 = 11
Determine
225 = 15
Determine
400 = 20
Ex1: Simplify
75
25
5
3
3
Explain
 Determine the
perfect square
factor.
 Write both
factors with
radicals (perfect
square goes 1st).
 Take the square
root of the perfect
square.

Simplify
45
9
3
5
5
Simplify
24
4
2
6
6
Simplify
50
25
5
2
2
Simplify
98
49
7
2
2
Ex3: Simplify
 Determine the
perfect square factor.
-5 12
-5 4
Explain
3
-5  2 3
-10 3
 Bring down the
number outside the
radical.
 Write both factors
with radicals.
 Take the square
root of the perfect
square and multiply
it by outside number.

Simplify
4 27
4
9
3
43 3
-12 3
Simplify
-3 125
-3 25 5
-3  5 5
-15 5

Simplify
-8
36
-8  6
-48
Simplify
7
7
40
4
10
7  2 10
14
10
Ex3: Simplify
Explain
72
 Determine the
LARGEST perfect
square factor.
36
6
2
2
 Write both factors
with radicals.
 Take the square
root of the perfect
square.
 If number inside
radical can be divided
by a perfect square
keep simplifying.

Ex3: Simplify
Explain
72
 Determine the
LARGEST perfect
square factor.
9
8
3
8
3 4
3 2
2
2
6
2
 Write both factors
with radicals.
 Take the square
root of the perfect
square.
 If number inside
radical can be divided
by a perfect square
keep simplifying.

Simplify
48
48

4
12
2
12
16
4 3
2 4
2 2
3
3
4
3
3
Simplify
128
128
16 8
64
4
8
8
4 4
4 2
2
2
8
3
2
2
Simplify
80
80
4
20
16
2
20
4
2 4
2 2
5
5
4
5
5
5
Simplify
-5
200
-5 100 2
-5  10
2
-10 2
Simplify
7
108
7
36
3
7  6
3
42
3
Simplify
-3
81
-3  9
-27
Tips for the lesson
 Have students record vocabulary and examples in their notes. They should do
guided practice on scratch paper or on whiteboards. If you want to grade guided
practice as part of their classwork grade have them staple it and hand it in with
their classwork or homework. Use guided practice time to call on students and
assess the class.
 There are multiple ways to teach this including using a factor tree. I like the table
method the best because students eventually memorize their perfect squares and
stop having to reference the table. Also, I believe students can’t affectively use a
factor tree when doing more complex problems such as adding, subtracting,
multiplying, and dividing expressions with multiple radicals.
 I allow students to use calculators with this lesson so they can figure out how
to use the square root sign on the calculator. Also, allows them to radicals with
larger numbers and they use it to guess & check perfect square factors.
Eventually, like the table of perfect squares, students stop needing to use the
calculator as they get more comfortable.
 Some students have a difficult time with this topic and giving lots of practice and
feedback when they make mistakes will help. The class as a whole will get better
as you build on this with each lesson.