Name: __________________________
Algebra 1-1: Lesson 9
Goal – Find square roots and compare real numbers.
Vocabulary
Square root: the “inverse” of squaring something. Since 52 = 25, the square root of 25 is 5.
Radical sign: what shows you’re taking the square root. “The square root of 25” is written √25.
Radicand: the expression inside the radical symbol. The radicand of √25 = 5 is 25 because it is
inside the radical sign.
Perfect square: the square of an integer. 25 is a perfect square because 52 = 25, but 5 is NOT a
perfect square because there’s no integer that you can square to get it.
Integer: a positive or negative whole number.
MEMORIZE THIS TABLE
Which is the same as…
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
USE THIS TABLE
(but you don’t need to memorize it)
Which is the same as…
112
122
132
142
152
162
172
182
192
202
= 121
= 144
= 169
= 196
= 225
= 256
= 289
= 324
= 361
= 400
√121 = 11
√144 = 12
√169 = 13
√196 = 14
√225 = 15
√256 = 16
√289 = 17
√324 = 18
√361 = 19
√400 = 20
There are actually TWO
square roots for each number.
Since (−2)(−2) = 4
the real √4 = 2 𝐴𝑁𝐷 − 2.
You can write: √4 = ±2.
~~Lesson 9: Find square roots and compare real numbers.~~
EXAMPLE 1
Find the square root of a perfect square
Evaluate the expression without using a calculator.
a. √400
b. √16
c. √81
Solution:
End goal: get both a positive and a negative number
NOTICE!
Since you have
taken the square
root of a number,
the radical sign
disappears.
a.
√400
±20
b. √16
±4
c. √81
±9
Find the radicand on the square root table and see what its positive square root is.
Write both the positive AND negative values for the square root.
 Answer!
Find the radicand on the square root table and see what its positive square root is.
Write both the positive AND negative values for the square root.
 Answer!
Find the radicand on the square root table and see what its positive square root is.
Write both the positive AND negative values for the square root.
 Answer!
Exercises for Example 1
Evaluate the expression without using a calculator.
1. √289
EXAMPLE 2
2. √100
3. √196
Approximate a square root
Approximate √𝟓𝟐 to the nearest integer without using a calculator.
Solution:
End goal: get an integer
√52
√52 is in between √49 and √64
Check if 52 is on the square root table. It is not, so find the two
number on the table that it is between.
52 − 49 = 3 and 64 − 52 = 12
Figure out the difference between 52 and each of those numbers.
√52 is closer to √49
Since 52 is closest to 49, √52 will be closest to √49, which is 7.
√52 ≈ 7
 Answer!
~~Lesson 9: Find square roots and compare real numbers.~~
Exercises for Example 2
Approximate the square root to the nearest integer without using a calculator.
4. √75
5. √240
6. √20
1. What is this section about?
2. What is one important idea in this section?
3. What is one mistake that someone might make when trying to do these kinds of problems?
Extra Practice:
You must complete the circled problems before you take your knowledge celebration.
You may complete as many of the others as you need to feel comfortable with the material.
Write the number as a power.
1. 36
2. 100
Evaluate the expression without using a calculator.
4. √49
5. √4
3. 9
6. √25
~~Lesson 9: Find square roots and compare real numbers.~~
7. √81
8. √121
9. √16
Approximate the square root to the nearest integer without using a calculator.
10. √19
11. √28
9. √5
12. √53
13. √138
14. √70
Was the problem completed correctly? If not, find and correct the error.
15. √25
16. √50
±√5
±25
Complete the word problems using the material from the section.
17. A local park is in the shape of a square and covers an area of 3600 square feet. Find the side length of the park.
18. You are considering buying a square wall poster that has an area of 6.25 square feet. Find the side length of the wall
poster.