Answer
a) $2$
b) $2^2$
Work Step by Step
a) We know that the RMS speed is given by
$$v_{\rm rms}=\sqrt{(v_{avg})^2}$$
Let's assume we have $N$ number of molecules, so the average speed of them is given by
$$v_{avg}=\dfrac{v_1+v_2+...+v_N}{N}$$
Increasing the speed of each molecule by a factor of 2 means increasing the total average speed by 2.
$$v_{avg}'=\dfrac{2v_1+2v_2+...+2v_N}{N}=2\dfrac{v_1+v_2+...+v_N}{N}=2v_{avg}$$
Hence, the RMS speed then is
$$v_{\rm rms}=\sqrt{(v_{avg}')^2}=\sqrt{(2v_{avg})^2}$$
$$v_{\rm rms}=2\sqrt{(v_{avg})^2}$$
So, the RMS speed increased by a factor of 2.
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b) We know that the pressure due to the force of the molecules colliding with the walls is given by
$$P=\dfrac{Nm }{3V}v_{\rm rms}^2$$
So when the RMS speed increases by a factor of 2, the pressure increases by a factor of $2^2=4$ since $P\propto v_{\rm rms}^2$