[tex]a) \sqrt{248} = \sqrt{2 \times 2 \times 2 \times 31} = \sqrt{(2 \times 2) \times 2 \times 31} = \sqrt{ {2}^{2} \times 2 \times 31 } = 2 \sqrt{2 \times 31} = 2 \sqrt{62} [/tex]
[tex]b) \sqrt{1260} = \sqrt{2 \times 2 \times 3 \times 3 \times 5 \times 7} = \sqrt{(2 \times 2) \times (3 \times 3) \times 5 \times 7} = \sqrt{ {2}^{2} \times {3}^{2} \times 5 \times 7 } = (2 \times 3) \sqrt{5 \times 7} = 6 \sqrt{35} [/tex]
[tex]c) \sqrt{1620} = \sqrt{2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 5} = \sqrt{(2 \times 2) \times (3 \times 3) \times (3 \times 3) \times 5} = \sqrt{ {2}^{2} \times {3}^{2} \times {3}^{2} \times 5 } = (2 \times 3 \times 3) \sqrt{5} = 18 \sqrt{5} [/tex]
[tex]d) \sqrt{2250} = \sqrt{2 \times 3 \times 3 \times 5 \times 5 \times 5} = \sqrt{(3 \times 3) \times (5 \times 5) \times 2 \times 5} = \sqrt{ {3}^{2} \times {5}^{2} \times 2 \times 5 } = (3 \times 5) \sqrt{2 \times 5} = 15 \sqrt{10} [/tex]
[tex]e) \sqrt{5760} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5} = \sqrt{(2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times 2 \times 5} = \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} \times {3}^{2} \times 2 \times 5 } = (2 \times 2 \times 2 \times 3) \sqrt{2 \times 5} = 24 \sqrt{10} [/tex]
[tex]f) \sqrt{882} = \sqrt{2 \times 3 \times 3 \times 7 \times 7} = \sqrt{(3 \times 3) \times (7 \times 7) \times 2} = \sqrt{ {3}^{2} \times {7}^{2} \times 2 } = (3 \times 7) \sqrt{2} = 21 \sqrt{2} [/tex]
