Question 759814: how to find decimals from radical ? plz solve this one √27
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! how to find decimals from radical ? plz solve this one √27
-----
Note: 27 is not a perfect square. Therefore, it's square
root is an irrational number. Irrational numbers can only
be approximated using decimal notation.
----
sqrt(27) = sqrt(9*3) = 3sqrt(3) = 3(1.7321...) = 5.1962...
====================================
Finding sqrt(3)
Since 3 is between 1 and 4, sqrt(3) is between sqrt(1) and sqrt(4).
So, sqrt(3) is at least 1 and it is less than 2.
---
Try sqrt(3) = 1.5
1.5^2 = 2.25 which is less than 3
Try sqrt(3) = 1.75
1.75^2 = 3.0625 which is very close to 3
---
At this point you could try 1.74
1.74^2 = 3.0276 which is even closer to 3
---
Try 1.73^2 = 2.9929
--
Now you know 1.73 < sqrt(3)< 1.74
---
You could carry this on forever to get addition decimal places,
but you will never be able to find a decimal form for sqrt(3)
======
Hope that helps.
Cheers,
Stan H.
=================
|
|
|
