R-squared threshold for an F test

Consider the multiple linear regression model $y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \epsilon_i$, $i = 1,2,…,25$, where $\beta_0, \beta_1$ and $\beta_2$ are unknown parameters, $\epsilon_i$'s are uncorrelated random errors with mean 0 and finite variance $\sigma^2 > 0$. Let $F_{\alpha,m,n}$ be such that $P(Y > F_{\alpha,m,n}) = \alpha$, where $Y$ is a random variable having an $F$-distribution with $m$ and $n$ degrees of freedom. Suppose that testing $H_0: \beta_1 = \beta_2 = 0$ against $H_1$: At least one of $\beta_1, \beta_2$ is not 0 involves computing $F_0 = 11 \frac{R^2}{1-R^2}$ and rejecting $H_0$ if the computed value $F_0$ exceeds $F_{\alpha,2,22}$. Given that $F_{0.025,2,22} = 4.38$, $F_{0.05,2,22} = 3.44$, the smallest value of $R^2$ that would lead to rejection of $H_0$ for $\alpha = 0.05$ equals ________ (rounded off to two decimal places).