1. Given two perpendicular forces:
F_1 = 6\, \text{N}
F_2 = 4\, \text{N}
2. Use the Pythagorean theorem to find the total force:
F_{\text{total}} = \sqrt{F_1^2 + F_2^2}
3. Substitute the values:
F_{\text{total}} = \sqrt{6^2 + 4^2}
F_{\text{total}} = \sqrt{36 + 16}
F_{\text{total}} = \sqrt{52}
F_{\text{total}} = 2\sqrt{13} \, \text{N}
Answer:
2\sqrt{13} \, \text{N}