" (2) If "sqrt(2)=1.41," then "(1)/(sqrt(2))=?

If sqrt(2)=1.41 and sqrt(5)=2.24, find the value of (3)/(8sqrt(2)+5sqrt(5))+(2)/(8sqrt(2)-5sqrt(5))

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

Prove that : (1)/(sqrt(2)+1)+ (1)/(sqrt(3)+sqrt(2))+ (1)/(2+sqrt(3))=1

Sum the series to infinity : sqrt(2)- (1)/(sqrt(2))+(1)/(2(sqrt(2)))-(1)/(4sqrt(2))+ ....

Which term of the sequence sqrt2, (1)/(sqrt2), (1)/(2 sqrt2) ……is (1)/(512 sqrt2) ?

Evaluate : 1/( 1 + sqrt (2) ) + 1/( sqrt(2) + sqrt (3) ) + 1/ ( sqrt(3) + sqrt (4) )