In this lesson and we are going to
estimate square roots that have an irrational value
by using a number line and a guess and check method.
As an example we are going to estimate √5.
I cannot think of a number that when multiplied by itself equals five;
however, I know that 2^2=4.
So √4 = 2.
Notice that I have put the √4  above the number 2 on the number line.
I also know that 3^2 = 9, so √9 = 3
Again I have placed the √9 on the number line this time above the 3.
Now I can see that the √5 must be between 2 & 3 because 5 is between 4 & 9
I'd like to be a little more precise with my measurement and estimate the √5 to the tenths place.
I see that 5 is closer to 4 than it is to
9, so first I'm going to guess and check by squaring 2.1
2.1^2 = 4.41.
This is close to 5, but I'm going to see if I can get closer.
Let's try 2.2 squared.  2.2^2 = 4.84.
This is even closer to 5, but
it's still too small.
Let's try 2.3 squared.
2.3^2 = 5.29.  Ooops this is too big.
So now I can say, the √5 is between 2.2 and 2.3.
