$\left|V_{\text {rel }}\right|=\sqrt{V^{2}+V^{2}-2(V)(V) \cos \theta}$

$=2 V\left|\sin \frac{\theta}{2}\right|$

This implies,

$\left\langle V_{\text {rel }}\right\rangle=\frac{\int_{0}^{\pi} 2 V\left|\sin \frac{\theta}{2}\right| d \theta}{\int_{0}^{\pi} d \theta}$

$=\frac{4 V}{\pi}$

Thus,

$\left\langle V_{\text {га }}\right\rangle=\frac{4}{\pi} V_{\text {average}}$

$=\frac{4}{\pi} \sqrt{\frac{8 R T}{\pi m_{0}}}$ $....(I)$

Substitute the values in equation $(I).$

$\left\langle V_{\text {гel }}\right\rangle=\frac{4}{\pi} \sqrt{\frac{8 \times 8.3 \times 300}{3.14 \times 28 \times 10^{-3}}}$

$=606 \,m / sec$