Download square roots

SQUARE ROOTS
Principle square roots – Imperfect square roots
 A square root is the product of 2 identical numbers
Example: the square of 7 is (72) which is equal to 7 x 7 = 49
Activity:
a) 92
e) 122
b) 112
f) 62
c) 42
g) the square of 30 =
d) 172
h) 72 - 62 =
i) 2(4)2 + 3(22) =
m) 50 – 32 x 5 =
j) 6(32) - 2(52) =
n) 6 x 52 -- 5 x 42
k) 12 + 22 = 32 =
o) 16 + 3 x 72
l) 8 x 32 12 =
Finding the Square Root is the opposite of finding the
square.
52 = 5 x 5 = 25
25 = 5
100 means _____ x _____ = 100
these two numbers must be the same
ACTIVITY: Do together orally)
a) 144
12
122 = 144
b) 36
6
62 = 36
c) 400
d) 16
e) 64
20
4
8
202 = 400
42 = 16
82 = 64
 Have the students write the squares from 1 – 25
Square Roots
Perfect square – imperfect square roots
Principle square root
 One of two equal factors of a number.
Example:

The 16 = 4 x 4
Any positive real number has two square roots.
Example:
The 16 = 4 and – 4
Because
4 x 4 = 16 and - 4 x - 4 = 16
The positive square root is called the Principle Square
Root.
Example:
The square root of 25 is real +25 and -25
The principle square root of 25 is +25
 There are 4 ways to calculate square root (
Calculator
Mental computations
).
Estimating
Factoring (prime factorization)
ACTIVITY:
1.
100 - 49
=
_________________________
2.
64 + 36
=
_________________________
3.
49 - 81
=
_________________________
4.
5.
1 - 25 + 64
36 - 144 =
=
__________________
_________________________
ESTIMATING SQUARE ROOTS.
Most numbers like 85, do not have a perfect square
root. Example:
The square root of 81 = 9
The square root of 100 = 10
The square root can be approximated using a
divide-and- average method.
To find the square root of a number accurate to a
specific number of decimal places, follow these steps:
1. Estimate the integer whose square is closest to the number.
2. Divide the number by your estimate and calculate a
quotient with two more decimal places than the divisor (the
estimate).
3. Find the average of the divisor (estimate) and the quotient.
Ex: Find the positive square root of 85 to the nearest hundredth.
1.
Estimate 9, because 9 x 9 = 81
2.
85 = 9.44
9
3.
9 + 9.44 = 9.22
2
The square root of 85 = 9.22 (to the nearest hundredth)
ACTIVITY:
Estimate the integer whose square is closest to the number.
a)
50
__________________
b)
150
__________________
c)
500
__________________
d)
1500
__________________
Find the positive square root to the nearest hundredth.
a)
28
b)
72
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Find the positive square root to the nearest thousandth.
a)
2
b)
5
c)
12
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