[tex] \sqrt{45} = \sqrt{3 \times 3 \times 5} = \sqrt{(3 \times 3) \times 5} = \sqrt{ {3}^{2} \times 5 } = 3 \sqrt{5} [/tex]
[tex] \sqrt[3]{250} = \sqrt[3]{2 \times 5 \times 5 \times 5} = \sqrt[3]{(5 \times 5 \times 5) \times 2} = \sqrt[3]{ {5}^{3} \times 2 } = 5 \sqrt[3]{2} [/tex]
[tex] \sqrt[4]{162} = \sqrt[4]{2 \times 3 \times 3 \times 3 \times 3} = \sqrt[4]{(3 \times 3 \times 3 \times 3) \times 2} = \sqrt[4]{ {3}^{4} \times 2 } = 3 \sqrt[4]{2} [/tex]
[tex] \sqrt{2000} = \sqrt{2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5} = \sqrt{(2 \times 2) \times (2 \times 2) \times (5 \times 5) \times 5} = \sqrt{ {2}^{2} \times {2}^{2} \times {5}^{2} \times 5 } = (2 \times 2 \times 5) \sqrt{5} = 20 \sqrt{5} [/tex]
