Question

how to solve 8th and 9th question?

Answer 1

for 8th question
take that number as x
x=32.123535.....
now multiply it by 100
100x=3212.3535.... (|)
then multiply it by 10000
10000x=321235.3535.... (||)

(||)-(|)
9900x=318023--------( don't believe my calculations try yourself)

therefore
x=318023/9900

Answer 2

Q.8
Let x= 32.12353535...
So 100x= 3212.353535...
And 10000x= 321235.353535...
Now subtracting 100x from 10000x,
9900x= 321235.353535...-3212.353535...
= 321235-3212= 318023
So x= 318023/9900

Q.9
a= 6+ 2√3
So 1/a= 1/(6+2√3)
= (6-2√3)/(6+2√3)(6-2√3)
=(6-2√3)/(6^2-(2√3)^2)
=(6-2√3)/(36-12)
=(6-2√3)/24
=(3-√3)/12
So a+1/a= 6+2√3 - (3-√3)/12
= [(6+2√3)12-3+√3]/12
=(72+24√3-3+√3)/12
=(69+25√3)/12