Answer
$H_2 : 1.90 \times 10^3 \space m/s$
$O_2 : 478 \space m/s$
Work Step by Step
$$v_{rms} = \Bigg( \frac{3RT}{M} \Bigg)^{1/2}$$ $$R = 8.3145 \space JK^{-1}mol^{-1}$$ $$20^o \space C = (20 + 273)K = 293 \space K$$
$H_2$:
$M = 2*1.01 = 2.02 \space g/mol = 0.00202 \space kg/mol$
$$v_{rms} = \Bigg( \frac{3(8.3145 \space JK^{-1}mol^{-1})(293 \space K)}{0.00202 \space kg/mol} \Bigg)^{1/2}$$ $$v_{rms} = 1.90 \times 10^3 \space m/s$$
$O_2$:
$M = 2*16.0 = 32.0 \space g/mol = 0.0320 \space kg/mol$
$$v_{rms} = \Bigg( \frac{3(8.3145 \space JK^{-1}mol^{-1})(293 \space K)}{0.0320 \space kg/mol} \Bigg)^{1/2}$$ $$v_{rms} = 478 \space m/s$$
