The administrator should use the following three commands to resolve the issue of the root filesystem being full:

df -h /. This command will show the disk usage of the root filesystem in a human-readable format. The df command is a tool for reporting file system disk space usage. The -h option displays the sizes in powers of 1024 (e.g., 1K, 234M, 2G). The / specifies the root filesystem. The command df -h / will show the total size, used space, available space, and percentage of the root filesystem. This command will help the administrator identify the problem and plan the solution.

growpart /dev/mapper/rootvg-rootlv. This command will grow the partition that contains the root filesystem to the maximum size available. The growpart command is a tool for resizing partitions on Linux systems. The /dev/mapper/rootvg-rootlv is the device name of the partition, which is a logical volume managed by the Logical Volume Manager (LVM). The command growpart /dev/mapper/rootvg-rootlv will extend the partition to fill the disk space and increase the size of the root filesystem. This command will help the administrator solve the problem and free up space.

lvresize –L +10G -r /dev/mapper/rootvg-rootlv. This command will resize the logical volume that contains the root filesystem and add 10 GB of space. The lvresize command is a tool for resizing logical volumes on Linux systems. The -L option specifies the new size of the logical volume, in this case +10G, which means 10 GB more than the current size. The -r option resizes the underlying file system as well. The /dev/mapper/rootvg-rootlv is the device name of the logical volume, which is the same as the partition name. The command lvresize –L +10G -r /dev/mapper/rootvg-rootlv will increase the size of the logical volume and the root filesystem by 10 GB and free up space. This command will help the administrator solve the problem and free up space.

The other options are incorrect because they either do not affect the root filesystem (fdisk -1 /dev/sdb, pvcreate /dev/sdb, lsblk /dev/sda, or vgextend /dev/rootvg /dev/sdb) or do not use the correct syntax (fdisk -1 /dev/sdb instead of fdisk -l /dev/sdb or parted -l /dev/mapper/rootvg-rootlv instead of parted /dev/mapper/rootvg-rootlv print). References: CompTIA Linux+ (XK0-005) Certification Study Guide, Chapter 10: Managing Storage, pages 318-319, 331-332.