Estimate startroot 37 endroot 37 to the nearest tenth. then locate startroot 37 endroot 37 on a number line.

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.

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these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation: