how to solve the square root of 23-(which is not a perfect square)
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:
- Find the nearest perfect squares around 23.
- Notice that 23 is between 16 and 25.
- Since it’s closer to 25, choose a number closer to 5 than to 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.