Question

in which section of the number line is √17

Answer 1

$\bf \sqrt{17}\approx 4.123 \\\\[-0.35em] ~\dotfill\\\\ \boxed{4}\rule[0.35em]{2em}{0.25pt}\stackrel{\sqrt{17}}{4.123}\rule[0.35em]{10em}{0.25pt}\boxed{5}\qquad \leftarrow \textit{between 4 and 5}$

Answer 2

We want to see in which section of the number line is √17

We will see that √17 is between 4 and 5 on the number line.

To see this, we can estimate two consecutive whole numbers such that one is smaller than √17 and the other is larger.

The smaller number is 4, because:

4*4 = 16

then:

√16 = 4

So we have:

4 = √16 < √17

And on the other end we have:

5*5 = 25

√17 < √25 = 5

Then we can write:

4 < √17 < 5

So we know that √17 is between 4 and 5 (more closer to 4 than 5) on the number line.

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