Question

What is square root of 28 approximated to the nearest tenth?

Answer 1

Say to yourself - which whole numbers does the square root of 28 lie between.
Well 5 x 5 = 25  and 6 x 6 = 36.   So it lies between 5 and 6 and because 28 is a little closer to 25 than it is to 36, we should guess a number that is less than 5.5.

It doesn't matter whether I chose 5.4, 5.3, 5.2 or 5.1 but my best guess would be about 5.2 or 5.3.  I already know which is the better of the two having used a calculator.  But instead I am going pretend I don't have one handy and I will use 5.2
Now I will divide 28 by 5.2     28/5.2=5.38 rounded to the nearest hundredth.
Now I will find the average of my divisor (5.2) and my answer 5.38
(5.2+5.38)/2 = 5.29  I will use that number (5.29) as my new divisor
28/5.29 = 5.293 rounded.   I already have enough information to round the square root of 28 to the nearest tenth.  It will be 5.3 since the 9 is large enough 
 to round the 2 to a 3.  5.3 is the answer.
We could continue to average the answer and the divisor and use the new number to round the square root of 28 to the nearest 100th, 1000th and so on, but because the square root of 28 is irrational, we will never get an exact answer.  There is no number times itself that equals 28.