Download 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?