The square root of 23 is about 4.796. Since 23 is not a perfect square, its square root is irrational, so you usually write it as 23\sqrt{23}23​ or give a decimal approximation.

Quick Scoop

Here’s the simple way to think about it:

  • 42=164^2=1642=16
  • 52=255^2=2552=25

So 23\sqrt{23}23​ must be between 4 and 5. Because 23 is closer to 25 than to 16, a good estimate is about 4.8.

More Exact Value

If you want a more precise decimal, the value is:

  • 23≈4.7958315\sqrt{23}\approx 4.795831523​≈4.7958315.

Easy Method

A quick estimate method is:

  1. Find the nearest perfect squares around 23.
  2. Notice that 23 is between 16 and 25.
  3. Since it’s closer to 25, choose a number closer to 5 than to 4.
  4. A good classroom estimate is 4.8.

Mini Example

To check the estimate:

  • 4.82=23.044.8^2=23.044.82=23.04

That is very close to 23, so 4.8 is a solid approximation.

TL;DR: 23\sqrt{23}23​ is approximately 4.796 , and a fast estimate is 4.8.