Find Square and Cube Roots
and Compare Real Numbers
Math 8
Unit 1
Section 2.7
Learning Targets
• I will classify numbers as whole, integer, rational, irrational,
and/or real
• I will compare and order real numbers.
• I will determine the square root of a perfect square number
up to 144 without a calculator.
• I will determine the cube root of a perfect cube number up to
125 without a calculator.
• I will approximate square roots up to 144 without a
calculator.
• I will determine the square root of a number using a
calculator.
Vocabulary
• Square Root – if 𝑏2
42 = 16;
= 𝑎, 𝑡ℎ𝑒𝑛 𝑏 𝑖𝑠 𝑎 𝑠𝑞𝑢𝑎𝑟𝑒 𝑟𝑜𝑜𝑡 𝑜𝑓 𝑎.
16 = 4 𝑜𝑟 − 4
• Radical symbol -√
• Radicand – the number or expression inside a radical
symbol. 16; 16 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑎𝑑𝑖𝑐𝑎𝑛𝑑
• Perfect Square – The square of any integer. 32
42 = 16
= 9,
Vocabulary
• Cube Root – if 𝑏3
3
3 = 27;
3
= 𝑎, 𝑡ℎ𝑒𝑛 𝑏 𝑖𝑠 𝑎 𝑐𝑢𝑏𝑒 𝑟𝑜𝑜𝑡 𝑜𝑓 𝑎
27 = 3
• Perfect Cube – The cube of any integer.
23 = 8; 33 = 27; 43 = 64
Vocabulary
• Irrational number – a number that cannot be written as
a quotient of two integers. The decimal form of an
irrational number neither terminates nor repeats.
• Real numbers – the set of all rational and irrational
numbers.
Find Square Root
Perfect Squares
Integer Square
1
1
2
4
3
9
4
16
5
25
6
36
Integer Square
7
49
8
64
9
81
10
100
11
121
12
144
Approximate a Square Root
When a radicand is a whole number that is not a perfect
square you must approximate.
Approximate the square root of 136. 136
• Determine the perfect squares above and below
121 = 11, 144 = 12
•
The 136 is between 11 and 12
136 is closer to 144 than 121 so,
the square root of 136 is about 12
Classify Numbers
Graph and Order Real Numbers
Find a Cube Root
Evaluate the expression
3
27 = 3
3
3 = 27
3 × 3 × 3 = 27
Perfect Cubes
Integer
1
2
3
4
5
Cubes
1
8
27
64
125