Approximating Square and Cube Roots

Estimating Square and Cubic Roots

​ALEF Lessons 19 & 20

Learning Objectives:

​

​- To estimate square and cube roots on a number line

​

​- To estimate square and cube roots to the nearest tenth

Starter:​

Answer the following 5 questions on square roots and cube roots.​

Multiple Choice

√100

• 15
• 10
• 11
• 12

Multiple Choice

Evaluate √64

• 3
• 8
• 7
• 6

Multiple Choice

200  __________

• is a perfect square

• is not a perfect square

Multiple Choice

Which number is both a perfect square and a perfect cube?

• 64

• 27

• 81

• 16

​Let's recap square roots and cube roots

​Square Roots:

​Cube Roots:

​Estimating Square and Cube Roots on a number line

​Approximating square roots:

​

To find the square root of a number that is not a perfect square, it will be necessary to find an approximate answer by using the following methods.

​Example:

Multiple Choice

Identify the two consecutive integers in which the square root lies between: $$\sqrt{95}$$  

• 8 and 9

• 9 and 10

• 10 and 11

• 11 and 12

Multiple Choice

Identify the two consecutive integers in which the square root lies between: $$-\sqrt{17}$$  

• -4 and -5

• -5 and -6

• -6 and -7

• -7 and -8

Multiple Choice

Identify the two consecutive integers in which the square root lies between: $$-\sqrt{156}$$  

• -9 and -10

• -10 and -11

• -11 and -12

• -12 and -13

Multiple Choice

Identify the two consecutive integers in which the square root lies between: $$\sqrt{48}$$  

• 4 and 5

• 5 and 6

• 6 and 7

• 7 and 8

Multiple Choice

In between what two integers is the square root of 77?

• 5 and 6
• 6 and 7
• 7 and 8
• 8 and 9

Multiple Choice

In between what two integers is the square root of 44?

• 3 and 4
• 4 and 5
• 5 and 6
• 6 and 7

Multiple Choice

Which two consecutive numbers is ∛30 in between

• 3 and 4

• 5 and 6

• 7 and 8

• 9 and 10

Multiple Choice

Which two consecutive numbers is ∛12 in between

• 3 and 4

• 7 and 8

• 2 and 3

• 5 and 6

Multiple Choice

Which two consecutive numbers is ∛192 in between

• 9 and 10

• 5 and 6

• 7 and 8

• 11 and 12

​Estimating Square and Cubic Roots to the nearest tenth

Watch ​ALEF Lesson 20 Apply Video

​Example 1:

​--->

​Example 2: Application

Multiple Choice

Will $$\sqrt[]{90}$$  be closer to 9 or closer to 10?

• 9

• 10

Multiple Choice

Will  $$\sqrt[]{41}$$  be closer to 6 or closer to 7?

• 6

• 7

Multiple Choice

Will  $$\sqrt[]{26}$$  be closer to 5 or closer to 6?

• 5

• 6

Multiple Choice

Will  $$\sqrt[]{51}$$  be closer to 7 or closer to 8?

• 8

• 7

Multiple Choice

Which number is an estimate to ∛186

• 5.8

• 5.5

• 5.7

• 5.1

Multiple Choice

Which number is an estimate to ∛58

• 4.2

• 4.1

• 3.8

• 3.9

Multiple Choice

Which number is an estimate to ∛10

• 2.3

• 2.0

• 2.1

• 2.2

Multiple Choice

Which number is an estimate to ∛163

• 5.7

• 5.9

• 5.6

• 5.5

Poll

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1. ​Time to work on ALEF Lessons 19 and 20

• ​Complete the Check Your Understanding Sections for ALEF Lesson 19

• ​Complete the Exit Ticket for ALEF Lesson 19

• ​​Complete the Check Your Understanding Sections for ALEF Lesson 20

• ​Complete the Exit Ticket for ALEF Lesson 20