Approximating Square Roots

I can approximate imperfect squares.

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. 

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. 

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.