Transcript square root
Square Roots
Presented by Mr. Laws
8th Grade Math, JCMS
CCSS Goal/Objective
8.EE.2 – Use square root and cube root
symbols to represent solutions to equations of
the form x2=p and x3=p, where p is a positive
rational number. Evaluate square roots of small
perfect squares and cube roots of small perfect
cubes.
Essential Question(s):
Using a math principle, how can we
find the square root of a number;
estimate the square root of number
between two consecutive integers;
and simplify irrational square roots?
What is a square root?
index
Radical sign
Square
Root
16 = 4
16 sq. ft
16
Radicand
4 roots
•Radical sign indicates a root.
•Radicand is the number under
the radical sign.
•Index displays the root of an
expression.
•The square root of a number is a number when
multiplied by itself equals the radicand.
Square Roots
Square roots are also written as this:
16 4
16 4
The square root of 16 can be positive or
negative 4 because:
4 4 4 16
16 4
(4) (4) (4) 16
16
2
2
Only the Radical
sign is negative!
No answer!!, Why?
Perfect Squares
Perfect squares are square roots when
multiplied by itself will equal an integer.
Perfect squares are rational numbers.
Examples:
1 1
25 5
81 9
169 13
4 2
36 6
100 10
196 14
9 3
49 7
121 11
225 15
16 4
64 8
144 12
256 16
Non-perfect Squares
Non-perfect squares are square roots that
are irrational numbers.
Calculators are also another way you can
identify non-perfect squares.
Examples:
2 1.4142135623...
6 2.4
5 2.2360679774...
80 8.94
Approx. to the
nearest 10th
Approx. to the
nearest 100th
Estimating Square Roots
You can also estimate square roots between
two consecutive integers.
Example: Find two consecutive integers
between the value of
.
74
The 74 is between the perfect squares of
64 and 81:
and 81 9
64 8
The two consecutive #’s that falls between the
74 is 8 and 9.
Estimating Square Roots
Estimate the value of
74
Where does it go on the
number line ?
Create a number line with the two consecutive numbers:
64
74
81
8
8.6
9
1. Guess and Check = 8.6 x 8.6
2. Try to get a number close to 74.
3. 8.6 x 8.6 = 73.96
74 8.6
Practice:
1. Find ea. square root.
a.
9
b.
16
49
c.
.81
d.
289
e.
400
2. Between what two consecutive integers does the following sq.
roots lies?
f.
g.
8
45
h.
137
i.
222
j.
321
3. Estimate the value of the following square roots (Round to nearest 10th:
k.
7
l.
24
m.
54
n.
110
0.
288
Question Review and Summary
Take a look over your notes; add questions
you may have missed.
Write down some important facts about the
lesson.
Summarized the lesson.
Is there something you don’t understand
about the lesson?
Can you answer the essential question?