Estimating value of √37.
We know that
and
, so
6 < √37 < 7
If we take the average of 6 and 7, we get
Since,
6 < √37 < 6.5
If we take the average of 6 and 6.5 , we get
Since,
6 < √37 < 6.25
If we take the average of 6 and 6.25 , we get
Since,
6 < √37 < 6.125
If we take the average of 6 and 6.125 , we get
Since,
6.0625 < √37 < 6.125
If we take the average of 6.0625 and 6.125 , we get
Since,
6.0625 < √37 < 6.09375
If we take the average of 6.0625 and 6.09375 , we get
Since,
6.078125 < √37 < 6.09375
If we take the average of 6.078125 and 6.09375 , we get
Since,
Therefore,
√37 ≈ 6.0859375.
And if we round it to the nearest tenth, we get
√37 ≈ 6.1
Locating √37 on number line.
In order to locate √37 on number line first draw a line 0 to 6 on number line.
Then draw a perpendicular line segment of 1 unit on number 6 on number line.
Join the number 0 on the number line by the top point of perpendicular line segment on number 6 we drew in above step.
Finally, draw a curve by taking radius as Hypotenuse of the right trinagle form in the diagram shown.
The curve would cut the number line exactly at √37 on number line.
