Approximating Square Roots

Approximating Square Roots

Learning Target

• I can approximate imperfect squares.

 $\sqrt{25},\ \sqrt{49},\ \sqrt{169}$  

We have been able to find the square root of perfect squares. 

 $\sqrt{51}$  

Today we will find the approximate square root of imperfect squares. 

Approximating Square Roots

• 
  
   $\sqrt{51}$  
  

• Find the two perfect squares 51 fits in between.

• The squares are 49 and 64

•  $\sqrt{49}\ \ \ \sqrt{51}\ \ \ \sqrt{64}$  

•  $7\ \ \ \sqrt{51}\ \ \ 8$  

• The  $\sqrt{51}$  is between 7 and 8. 

Approximating Square Roots

• 
  
   $\sqrt{12}$  
  

• Find the two perfect squares 12 fits in between.

• The squares are 9 and 16

•  $\sqrt{9}\ \ \ \sqrt{12}\ \ \ \sqrt{16}$  

•  $3\ \ \ \sqrt{12}\ \ \ 4$  

• The  $\sqrt{12}$  is between 3 and 4. 

Imperfect Squares

• The square root of imperfect squares are irrational numbers.

• Irrational numbers are numbers with decimals that neither repeat or terminate.

• They continue on and on without ending, much like  $\pi$  pi.  

Multiple Choice

Which square root an imperfect square?

• 
  

  $\sqrt{100}$
  

• $\sqrt{8}$

• $\sqrt{4}$

• $\sqrt{64}$

Multiple Choice

The square root of 20 can be found between which two consecutive integers?

• 0 and 2

• 10 and 20

• 5 and 6

• 4 and 5

Multiple Choice

 $\sqrt{72}\ is\ between\ which\ two\ integers?$  

• 3 and 5

• 8 and 9

• 7 and 2

• 7 and 8

Multiple Choice

Which is a perfect square?

• 
  

  $\sqrt{13}$
  

• $\sqrt{54}$

• $\sqrt{36}$

• $\sqrt{90}$