Approximating Square Roots

Estimating Square Roots

​Mr. Cerillo - Advanced Math

Remote Day - December 2024

You have already learned to find the square root of perfect squares. 

​Let's Review!!

List all of the perfect squares, on your paper, up to 169.

TODAY: You will find the approximate square root of imperfect squares. 

Approximating Square Roots

Approximating Square Roots

Multiple Choice

Between which two square roots does the √51 fall?

• √16 and √25

• √25 and √36

• √36 and √49

• √49 and √64

Multiple Choice

Between which two whole numbers does the √32 fall?

• 4 and 5

• 5 and 6

• 6 and 7

• 7 and 8

Multiple Choice

In between what two integers is the  $$\sqrt{44}$$  ?

• 3 and 4

• 4 and 5

• 5 and 6

• 6 and 7

Multiple Choice

The $$\sqrt{56}$$  is in between which two whole numbers?

• 1 and 2

• 3 and 4

• 5 and 6

• 7 and 8

Multiple Choice

The $$\sqrt{37}$$  is in between which two whole numbers?

• 1 and 2

• 3 and 4

• 6 and 7

• 7 and 8

Multiple Choice

The $$\sqrt{78}$$  is in between which two whole numbers?

• 10 and 11

• 11 and 12

• 9 and 10

• 8 and 9

Multiple Choice

$$Approximate\ \ \sqrt{8}\$$  

• 2.1

• 2.8

• 3.2

• 1.9

Multiple Choice

$$Approximate\ \sqrt{35}\$$  

• 5.9

• 5.2

• 6.3

• 4.8

Multiple Choice

$$Approximate\ \sqrt{30}\$$  

• 4.2

• 6.2

• 5.1

• 5.5

Multiple Choice

Which is the best estimate of ?

$$\sqrt{63}$$  

• 7.1

• 6.5

• 8.5

• 7.9

Multiple Choice

Estimate the following square root:

√13

• 5.6

• 2.6

• 3.1

• 3.6

Independent Practice

Multiple Choice

The area of a square is 36 cm².  What is the length of one side?

• 6 cm

• 9 cm

• 3 cm

• 18 cm

Multiple Choice

The area of a square picture frame is 100 cm².  What is the perimeter of the frame?

• 40 cm

• 25 cm

• 10 cm

• 50 cm

Multiple Choice

If I know the area of a square, how do I find the side length?

• 
  I square the area.

• 
  I divide the area by 2.

• 
  I divide the area by 4.

• 
  I take the square root of the area

Multiple Choice

A perfect square is a number whose square root is ___________.

• even

• 
  odd

• rational

• a never-ending

  (non-terminating) decimal

Multiple Choice

To find the square root of a number, you must divide it by 2.

• True

• False

Multiple Choice

The √20 is between which two consecutive integers?

• 2 & 3

• 4 & 5

• 
  3 & 4

• 5 & 6

Multiple Choice

x² = 121
What does x equal?

• 11²

• 20 and 11

• 11 and -11

• 11

Multiple Choice

Which number has a square root that is between 7 and 8?

• 48

• 60

• 81

• 36

Multiple Choice

The number 125 is...

• a perfect square.

• not a perfect square.

Multiple Choice

Square roots are the opposite of ____________.

• Cube Roots

• Multiplication

• Squaring

• Absolute Value