Need with understanding the hardy-weinberg principle:

a hypothetical population of 200 cats has two alleles, tl and ts, for a locus that codes for tail length. there are 60 cats with long tails (tltl genotype), 40 with medium (tlts genotype), and 100 with short tails (tsts genotype).
according to the answers, in the entire cat population, 60% of the alleles are ts. why is it so?
i tried solving it and i got 71%, here's how:
100/200=0.5
√(0.5)=0.7071 ~ 0.71
0.71*100=71%

where's the mistake?