how to identify a rational number with a square root between 3 and 4?

Question

Perfect squares are 3 and 4. I need help to figure out a rational number with a square root between 3 and 4 (not

perfect square, but a square root.) Can you show me how you got the answer too?

 

Also what square root of a number would be between 0.7 and 0.8?

Answer 1

OK.

Let's take 3 and 1/2 = 3.5

3 and 1/2 = 7/2

Squaring that, it is 7/2*7/2 = 49/4 = 12 and 1/4

3 < sqrt(49/4)=7/2 < 4


You can do the same with any mixed number between 3 and 4.
Please try it!!!


Likewise , we do the same for 0.7 = 7/10 = 70/100 AND 0.8 = 8/10 = 80/100

So any proper fraction between 70/100 and 80/100 will work.

A good choice is 75/100 = 3/4

Squaring that is 3/4*3/4 = 9/16

So 0.7 = sqrt(9/16)=3/4 = 0.75 < 0.8