can someone help me

Question

Is √2 between 1.4 and 1.5 ? How do you know?

Answer 1

Didi,

 

You know that if some number, call it x = √2, then x² must be equal to 2, x² = 2.  So let's test 1.4.

 

We multiply and find that 1.4 x 1.4 = 1.96, a little bit less than 2.  So no test 1.5, 1.5 x 1.5 = 2.25 which is a bit bigger than 2.  

 

So we can conclude that √2 lies somewhere between 1.4 and 1.5.  We might write that this way:

 

 1.4 < √2 < 1.5

 

 

Answer 2

Didi, 1.4 x 1.4 = 1.96 and 1.5 x 1.5 = 2.25, so the answer is yes.