Answer:
The square root of 2.5 is 1.58113883008419
√2.5 = 1.58113883008419
Proof that the square root of 2.5 is 1.58113883008419
The square root of 2.5 is defined as the only positive real number such that, multiplied by itself, it is equal to 2.5.
The square root of 2.5 can be written as (2.5)1/2. So,
(2.5)1/2 = (1.58113883008419 × 1.58113883008419)1/2
(2.5)1/2 = [(1.58113883008419)2]1/2
(2.5)1/2 = (1.58113883008419)2/2
(2.5)1/2 = (1.58113883008419)1
Thus,
√2.5 = 1.58113883008419
By coolconversion.com
See also, further on this page, how to calculate the square root of 2.5 using the Babylonian method
Step-by-step explanation:
Here is the answer to questions like: 2.5 square root? | √2.5 or what is the square root of 2.5?
Use the square root calculator below to find the square root of any imaginary or real number. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method.
The Babylonian Method also known as Hero's Method
See below how to calculate the square root of 2.5 step-by-step using the Babylonian Method also known as Hero's Method.
In this case we are going to use the 'Babylonian Method' to get the square root of any positive number.
We must set an error for the final result. Say, smaller than 0.01. In other words we will try to find the square root value with at least 1 correct decimal places.
Step 1:
Divide the number (2.5) by 2 to get the first guess for the square root .
First guess = 2.5/2 = 1.25.
Step 2:
Divide 2.5 by the previous result. d = 2.5/1.25 = 2.
Average this value (d) with that of step 1: (2 + 1.25)/2 = 1.625 (new guess).
Error = new guess - previous value = 1.25 - 1.625 = 0.375.
0.375 > 0.01. As error > accuracy, we repeat this step again.
Step 3:
Divide 2.5 by the previous result. d = 2.5/1.625 = 1.5384615385.
Average this value (d) with that of step 2: (1.5384615385 + 1.625)/2 = 1.5817307693 (new guess).
Error = new guess - previous value = 1.625 - 1.5817307693 = 0.0432692307.
0.0432692307 > 0.01. As error > accuracy, we repeat this step again.
Step 4:
Divide 2.5 by the previous result. d = 2.5/1.5817307693 = 1.5805471124.
Average this value (d) with that of step 3: (1.5805471124 + 1.5817307693)/2 = 1.5811389408 (new guess).
Error = new guess - previous value = 1.5817307693 - 1.5811389408 = 0.0005918285.
0.0005918285 <= 0.01. As error <= accuracy, we stop the iterations and use 1.5811389408 as the square root.
So, we can say that the square root of 2.5 is 1.581 with an error smaller than 0.01 (in fact the error is 0.0005918285). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(2.5)' is 1.5811388300841898.
Note: There are other ways to calculate square roots. This is only one of them.
