A red giant star radiates a power of 2.0 × 10²⁹ W from a surface at 3500 K…

Step 1. $\sigma T^4 = 5.67 \times 10^{-8}\ \text{W m}^{-2}\text{K}^{-4} \times (3500\ \text{K})^4 = 8.51 \times 10^{6}\ \text{W/m}^2$.

Step 2. $R = \sqrt{\dfrac{2.0 \times 10^{29}\ \text{W}}{4\pi \times 8.51 \times 10^{6}\ \text{W/m}^2}} = 4.33 \times 10^{10}\ \text{m}$.

Step 3. $\dfrac{4.33 \times 10^{10}\ \text{m}}{6.96 \times 10^{8}\ \text{m}} = 62$.