The Jiangmen Underground Neutrino Observatory (JUNO), a 20 kton multi-purpose low background liquid scintillator detector, was proposed primarily to determine the neutrino mass ordering. To suppress the radioactivity from the surrounding rocks and tag cosmic muons, the JUNO central detector is submerged in a water Cherenkov detector filled with 35 kton ultrapure water and equipped with 2400 20-inch microchannel plate photomultiplier tubes. Strict requirements are set for the intrinsic radioactivity of the ultrapure water, i.e., the $^{222}$Rn concentration should be less than 10 mBq/m$^3$. As the progenitor of $^{222}$Rn, the concentration of $^{226}$Ra should also be precisely measured and kept well below 10 mBq/m$^3$. In this proceeding, the details of two measuring systems, optimized to achieve a sensitivity of $\sim$1 mBq/m$^3$ for the radon concentration in water and of $\sim$13 $\mu$Bq/m$^3$ for the radium concentration in water, will be described.