Greatest lower bound

 The triangle PQR has a right angle at R.

The length of PQ is 4 cm, correct to the nearest centimetre.

The length of PR is 2 cm, correct to the nearest centimetre.

What is the greatest lower bound, in centimetres, of the length of QR?

• \(\sqrt{6} - \frac{1}{2}\)
• \(2\sqrt{3} - \frac{1}{2}\)
• \(2\sqrt{5} - \frac{1}{2}\)
• \(2\sqrt{5}\)
• \(2\sqrt{3}\)
• \(\sqrt{6}\)