Question 59689
The given expression is: 


rs(75 a^2)/ rs(5) 


75 can be written as 25 * 3 


==> rs(25 * 3 * a^2)/rs(5) 


==> [rs(25) * rs(3 * a^2)]/ rs(5)        {splitting of the radicals}


==> [5 * rs(3) * rs(a^2)]/ rs(5)          


{splitting of the radicals and rs(25) = 5}


==> [5 * rs (3) * a ]/ rs(5)          {rs(a^2) = a}


==> 5a* rs(3)/ rs(5) 
               

We know that 5 can be written as - rs(5)* rs(5)


Therefore, the above expression can be further simplified as:


==> [rs(5) * rs(5)* a * rs(3)]/ rs(5)


==> [rs(5)* a * rs(3)]  


{rs(5) gets cancelled both in the numerator and denominator}


==> rs(15) * a                   {By Multiplying radicals} 


==> rs(15) * a


is the solution to the given problem.


Regards,
Chitra