How do we divide by estimation

Consider,
Example below:

Let us find $\sqrt{7523}$ by division method.

Here, the remainder is 127. Therefore 7523 is not a perfect square.

Now, we know that

86² = 7396

and 87² = 7569

Now 7396 < 7523 < 7569

⇒ 86² < 7523 < 87²

$∴ 86 < \sqrt{7523} < 87$

Here, we can see that 7523 is must closer to 7569 than 7396.

Therefore, $\sqrt{7523}$ is approximately equal to 87.