Answer
7000 rads.
Work Step by Step
The table on page 901 shows that the Relative Biological Effectiveness (RBE) of $\alpha$ particles is about 20. The RBE of x-rays is 1.
This means that it requires 20 rads of x-rays to cause the same biological damage as 1 rad of $\alpha$ particles.
Therefore it takes 7000 rads of x-rays to cause the same biological damage as 350 rads of $\alpha$ particles.