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Unit2 #6
Name:_______________________________
Square Roots
Numbers such as 1, 4, 9, 16, and 25 are called _perfect squares_, because they are squares of whole #s.
A Square root of a number is one of its two equal factors.
4 · 4 = 16, so 4 is the _square root_ of 16.
The symbol
,called a _radical sign__ , is used to show a _POSITIVE_ square root.
Find each square root. Think…what times itself gives you 81? (? · ? = 81)
=9
= 14
=7
Every positive number has TWO square roots: positive and negative.
The symbol for negative square root is:
shows the _negative_ square root of 25.
Since (–5)² = 25, then
= –5
shows both _positive__ and _negative_ square root of 25.
= 5 and –5
= -9
= 14
=
7
= -11
If n² = a, then n =
c² = 9
b² = 169
m² = 289
c=
b=
m=
c=
b=
m=
To place 25 chairs in a square arrangement, how many chairs should be in each row?
=5
Moesha has 196 pepper plants that she wants to plant in square formation. How many pepper plants should
she plant in each row?
= 14
A new restaurant has ordered 64 tables for its outdoor patio. If the manager arranges the tables in a square
formation, how many will be in each row?
Area of a square is equal to the square of the length of a side.
A = s²
A miniature portrait of George Washington is square and has an area of 169 square centimeters. How long is
each side of the portrait?
= 13
The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of each
square.
Area =
Area =
Area =
144 square
inches
49 square
feet
324 square meters
= 12in side
P = 12 · 4 = 48 in
What is
? Think…what times itself gives you –25? (? · ? = –25) ___IMPOSSIBLE!____
Find each square root.
1.
5.
=4
2.
=
11
Solve each equation
d² = 64
d=
d=
= -3
6.
3.
imposs
7.
x² = 121
4.
8.
n² = 169
= -14
What if it is not a perfect square?
The square root of a number that is not a perfect square falls between two _consecutive whole numbers.
Step 1 Determine whether a number is a perfect square.
1. Is the number 29 a perfect square? Is there a whole number which can be squared to equal 29? _NO_
Step 2 Find the two consecutive whole numbers between which the
2. The number 25 is the closest perfect square _less_ than 29. What is
3. The number 36 is closest perfect square greater than 29. What is
4.
lies between
lies? _5 and 6____
and
lies.
? __5_
? _6__
. What are the two consecutive whole numbers between which
Find the two consecutive whole numbers between which the square root of a given number lies.
_4__ ___5___
__7____ __8____
__6____ ___7___
_______ _______
_______ _______
_______ _______
***Under what condition is
>
?
Spiral Review
1) The radius of the Sun is 6.96
meters. Write this distance in standard form.
Write each expression using exponents
2) 6 · 6 · 6
3) 2 · 3 · 3 · 2 · 2 · 2
4)
5) What is absolute value of -18?
6) 8 – 2(5) =
7) (–2)(3)(–5) =
Using the numbers 2, 3, and 4, write an example of the
8) Associative Property of Multiplication _______________________________ ;
9) Distributive Property _______________________________