Question

Estimate StartRoot 37 EndRoot 37 to the nearest tenth. Then locate StartRoot 37 EndRoot 37 on a number line.

Answer 1

Estimating value of √37.

We know that

$6^{2} = 36$ and $7^{2} =49$, so

6 < √37 < 7

If we take the average of 6 and 7, we get

$\frac{6+7}{2} = \frac{13}{2} = 6.5$

Since, $6.5^{2} = 42.25$

6 < √37 < 6.5

If we take the average of 6 and 6.5 , we get

$\frac{6+6.5}{2} = \frac{12.5}{2} = 6.25$

Since, $6.25^{2} = 39.0625$

6 < √37 < 6.25

If we take the average of 6 and 6.25 , we get

$\frac{6+6.25}{2} = \frac{12.25}{2} = 6.125$

Since, $6.125^{2} = 37.515625$

6 < √37 < 6.125

If we take the average of 6 and 6.125 , we get

$\frac{6+6.125}{2} = \frac{12.125}{2} = 6.0625$

Since, $6.0625^{2} = 36.75390625$

6.0625 < √37 < 6.125

If we take the average of 6.0625 and 6.125 , we get

$\frac{6.0625+6.125}{2} = \frac{12.125}{2} = 6.09375$

Since, $6.09375^{2} = 37.1337890625$

6.0625 < √37 < 6.09375

If we take the average of 6.0625 and 6.09375 , we get

$\frac{6.0625+6.09375}{2} = \frac{12.15625}{2} = 6.078125$

Since, $6.078125^{2} = 36.943603515625$

6.078125 < √37 < 6.09375

If we take the average of 6.078125 and 6.09375 , we get

$\frac{6.078125+6.09375}{2} = \frac{12.171875}{2} = 6.0859375$

Since, $6.0859375^{2} = 37.03863525390625$

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.