[tex] \sqrt{5000} = \sqrt{2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5} = \sqrt{(2 \times 2) \times (5 \times 5) \times (5 \times 5) \times 2} = \sqrt{ {2}^{2} \times {5}^{2} \times {5}^{2} \times 2 } = (2 \times 5 \times 5) \sqrt{2} = 50 \sqrt{2} [/tex]
