check if checkboxes in GridView are ticked

I have three checkboxes in a GridView but the user can only select one checkbox. So if they select the first checkbox, I need to alert them them that they cannot select the other two.

        <asp:GridView CssClass="tblResults" runat="server" ID="dgDetails" 
              OnRowDataBound="dgDetails_ItemDataBound" 
              DataKeyField="ID" AutoGenerateColumns="false"
             AlternatingRowStyle-BackColor="#EEEEEE">
             <HeaderStyle CssClass="tblResultsHeader" />
                <Columns> 
                    <asp:TemplateField HeaderText="Approved1">
                        <ItemTemplate>
                           <asp:CheckBox runat="server" ID="chkApproved1" />
                        </ItemTemplate>
                    </asp:TemplateField>
                   <asp:TemplateField HeaderText="Approved2">
                        <ItemTemplate>
                           <asp:CheckBox runat="server" ID="chkApproved2" />
                        </ItemTemplate>
                    </asp:TemplateField>
                   <asp:TemplateField HeaderText="Approved3">
                        <ItemTemplate>
                           <asp:CheckBox runat="server" ID="chkApproved3" />
                        </ItemTemplate>
                    </asp:TemplateField>
                  </Columns>
          </asp:GridView> 

code behind:

protected void dgDetails_ItemDataBound(object sender, GridViewRowEventArgs e)
    {
        if (e.Row.RowType == DataControlRowType.DataRow)
        {
            GridView gv = sender as GridView;
            Quote.QuoteDetails qd = e.Row.DataItem as Quote.QuoteDetails;

            CheckBox chkApproved1 = e.Row.FindControl("chkApproved1") as CheckBox;
            CheckBox chkApproved2 = e.Row.FindControl("chkApproved2") as CheckBox;
            CheckBox chkApproved3 = e.Row.FindControl("chkApproved3") as CheckBox;
       }
    }

I tried using something like this in query:

$('#<%= chkApproved1.ClientID %>').change(function () {
                if($(this).is(":checked")) {

                    }  
            });

But that causes the error:The name 'chkApproved1' does not exist in the current context.

So how can I check if the checkboxes in the GridView have been ticked?