notes completed

1. M8 Lesson 1-8 Square Roots - COMPLETED
1. Can you make a square out of 4 smaller squares? __Yes________
Side lengths: __2______ Area: ___4_________
2. Can you make a square out of 6 smaller squares? ___NO____
Side lengths: ___2 and 3_____ Area: __6_________
A number is called a ___square root_____ if it represents the side length of a square whose area is a
whole number. For example, 2 is a square root, because 2 represents the side length of a square whose
area is a whole number of 4.
A number is called a _____perfect square______ if it represents the area of a square whose side
length is a whole number. For example, 4 is a perfect square, because 4 square units represent the area of
a square with a side length of 2 units.
Side length: 5 in Side length: 10 cm Side length: 23 m
Area: 25 in2 Area: 100 cm2 Area: 529 m2
Therefore, each perfect square represents the __area_ of a square, and each root
represents the ___side length___.
This symbol is the radical and is asking, “what is the square root of” √ ?
1) √49 = 7 2) √121 = 11 3) √441 = 21 4) √289 = 17 5) √25 = 5
6) √225 = 15 7) √144 = 12 8) √576 = 24 9) √100 = 10 10) √324 = 18

2. Every positive number has _2__ square roots. One _positive__ and one _negative__. For example, one
square root of 16 is ___4____ since 4∙ 4 = 16. The other square root is ____-4_____ since (−4) ∙ (−4) = 16.
You can write the square roots of 16 as ±𝟒 meaning “plus or minus” 4.
Find the two square roots of each number:
1) 16 2) 81 3) 1 4) 100 5) 64
±𝟒 ±𝟗 ±𝟏 ±𝟏𝟎𝟎 ±𝟖
Evaluate the following problems.
1) √324 + √225 =
𝟏𝟖 + 𝟏𝟓
𝟑𝟑
2) √100 − 19 =
√𝟖𝟏
±𝟗
3) √
100
25
=
√𝟒
±𝟐
4) √144 + 3√81 =
𝟏𝟐 + 𝟑 ∙ 𝟗
𝟏𝟐 + 𝟐𝟕 = 𝟑𝟗
5) 2√100 − 3√16 =
𝟐 ∙ 𝟏𝟎 − 𝟑 ∙ 𝟒
𝟐𝟎 − 𝟏𝟐
𝟖
6) √64 + 36 =
√𝟏𝟎𝟎
±𝟏𝟎
7) 𝑥2
= 9
What number times itself is 9?
±𝟑
8) 𝑥2
= 25
What number times itself is 25?
±𝟓
9) 𝑦2
= 196
What number times itself is 196?
±𝟏𝟒
10) 81 = 𝑥2
What number times itself is 81?
±𝟗