# square root

```Lesson 9-1 Pages 436-440
Squares and
Square Roots
PA Lesson Check 7-Ch7
What you will learn!
1. How to find squares and
square roots.
2. How to estimate square
roots.
Perfect Square
Square root
What you really need to know!
A perfect square is the
square of a whole number.
A square root of a number is
one of two equal factors of
the number.
What you really need to know!
Every positive number has a
positive square root and a
negative square root.
The square root of a negative
number such as –25, is not
real because the square of a
number is never negative.
Square
Square Root
Example 1:
Find the square root:
64
Since
2
8
= 64,
64  8
Example 1b:
Find the square root:
 121
Since
2
11
= 121,
 121  11
Example 1c:
Find the square root:
 4
Since
2
2
= 4 and
2
(-2)
= 4,
 4  2 and  2
Example 2:
Use a calculator to fine the
square root to the nearest tenth.
23
23  4.79583152331271
4.8
Example 2b:
Use a calculator to fine the
square root to the nearest tenth.
 46
 46  6.78232998312527
-6.8
Example 3:
Estimate the square root to the
nearest whole number.
22
The perfect squares are:
1, 4, 9, 16, 25, 36, 49, 64, 81,
100, 121, 144, 169, ...
22 is between 16 and 25.
16  4 and 25  5
22
The perfect squares are:
1, 4, 9, 16, 25, 36, 49, 64, 81,
100, 121, 144, 169, ...
22 is closer to 25. So 5 is
the best estimate for the
square root of 22.
22  5
The perfect squares are:
1, 4, 9, 16, 25, 36, 49, 64, 81,
100, 121, 144, 169, ...
Example 3b:
Estimate the square root to the
nearest whole number.
 319
The perfect squares are:
..., 169, 196, 225, 256, 289,
324, 361, ...
319 is between 289 and 324.
289  17 and 324  18
 319
The perfect squares are:
..., 169, 196, 225, 256, 289,
324, 361, ...
319 is closer to 325. So 18
is the best estimate for the
square root of 319.
 319  18
The perfect squares are:
..., 169, 196, 225, 256, 289,
324, 361, ...
Example 4:
To estimate how far you can see
from a point above the horizon,
you can use the formula:
D  1.22  A
where D is the distance in miles
and A is the altitude, or height, in
feet.
Example 4:
The observations deck at the
Seattle Space Needle is 520
feet above the ground. On a
could a tourist see? Round
to the nearest tenth.
D  1.22  A
D  1.22  A
D  1.22  520
D  1.22  22.8035085019828
D  27.820280372419
D  27.8mi
Page 438
Guided Practice
#’s 4-11
Pages 436-438 with
someone at home and
study examples!
Homework: Pages 439-440
#’s 12-56 even, 71-80
Lesson Check 9-1
Homework: Pages 439-440
#’s 12-56 even
#’s 59, 60 and 71-74
Page
745
Lesson 9-1
Lesson Check 9-1
```