Creating new file with Square root of specific columns using awk - linux

Question

I have to find the square root of values in some specific columns in the file test.text and write the resulting column into another file. The file test.txt is shown below.
0004 0015 0018 0007 0015 0009 0003 0018 0012 0007 0013 0010 0018 0015 0002 0020 0007 0005
0010 0018 0015 0018 0007 0011 0010 0004 0013 0017 0016 0010 0019 0003 0002 0016 0005 0009
0002 0011 0015 0014 0008 0017 0002 0001 0015 0004 0008 0008 0002 0011 0015 0015 0009 0011
0013 0020 0005 0007 0007 0004 0019 0011 0001 0008 0013 0015 0015 0012 0007 0019 0009 0016
0003 0003 0020 0015 0007 0017 0005 0010 0012 0012 0009 0004 0016 0006 0014 0019 0001 0001
0014 0006 0016 0003 0008 0017 0002 0001 0011 0015 0014 0008 0016 0006 0014 0019 0012 0007
I have to find the square root of values from 2nd, 5th, 8th, 11th.. etc columns and write them into another file.
After searching, I have obtained the below code to print the square root of only one column.
awk '{r=$2; print "root=" sqrt(r)}' test.txt
This code prints only square root of column 2 values.
So I tried the below code using for loop.
awk 'BEGIN{FS=" "}{for(r=2;r<=NF;r+=3) printf sqrt($r)}' test.txt >newtest.txt
But still I am not getting the desired result as separate columns. I need newtest.txt file containing columns with square root values of 2nd , 5th, 8th ..etc columns of test.txt.
Any help regarding this will be appreciated.
Edit
The sample output I expect is newtest.txt which is shown below:
3.87298334621 3.87298334621 4.24264068712 3.60555127546 3.87298334621 2.64575131106
4.24264068712 2.64575131106 2.00000000000 4.00000000000 1.73205080757 2.23606797750
3.31662479036 2.82842712475 1.00000000000 2.82842712475 3.31662479036 3.00000000000
4.47213595500 2.64575131106 3.31662479036 3.60555127546 3.46410161514 3.00000000000
1.73205080757 2.64575131106 3.16227766017 3.00000000000 2.44948974278 1.00000000000
2.44948974278 2.82842712475 1.00000000000 3.74165738677 2.44948974278 3.46410161514

Answer 1

awk '{for(r=2;r<=NF;r+=3) printf("%.11f ",sqrt($r)); print ""}' test.txt >newtest.txt
Output to newtest.txt:
3.87298334621 3.87298334621 4.24264068712 3.60555127546 3.87298334621 2.64575131106
4.24264068712 2.64575131106 2.00000000000 4.00000000000 1.73205080757 2.23606797750
3.31662479036 2.82842712475 1.00000000000 2.82842712475 3.31662479036 3.00000000000
4.47213595500 2.64575131106 3.31662479036 3.60555127546 3.46410161514 3.00000000000
1.73205080757 2.64575131106 3.16227766017 3.00000000000 2.44948974278 1.00000000000
2.44948974278 2.82842712475 1.00000000000 3.74165738677 2.44948974278 3.46410161514