Hardy-Weinberg
The equilibrium model assumes a very large population, random mating, no selection, negligible mutation, and no migration. It is a comparison model for asking whether observed genotype frequencies match expected values. Allele frequency counts copies: heterozygotes contribute one copy of each allele. In a completely dominant system, the recessive phenotype identifies the recessive genotype, but the dominant phenotype combines two genotypes. A mismatch with expectations does not alone reveal which assumption failed.
If the recessive phenotype frequency is 0.09 and equilibrium applies, q=0.30, p=0.70, and the heterozygote frequency is 2pq=0.42. The square root is doing actual work here.
Do not plug the dominant phenotype frequency straight into p². Dominant-looking individuals may be homozygous or heterozygous.