[tex]a)\sqrt{450} = \sqrt{2 \times 3 \times 3 \times 5 \times 5} = \sqrt{(3 \times 3) \times (5 \times 5) \times 2} = \sqrt{ {3}^{2} \times {5}^{2} - 2 } = (3 \times 5) \sqrt{2} = 15 \sqrt{2} [/tex]
[tex]b) \sqrt{216} = \sqrt{2 \times 2 \times 2 \times 3 \times 3 \times 3} = \sqrt{(2 \times 2) \times (3 \times 3) \times 2 \times 3} = \sqrt{ {2}^{2} \times {3}^{2} \times 2 \times 3 } = (2 \times 3) \sqrt{2 \times 3} = 6 \sqrt{6} [/tex]
[tex]c) \sqrt{343} = \sqrt{7 \times 7 \times 7} = \sqrt{(7 \times 7) \times 7} = \sqrt{ {7}^{2} \times 7 } = 7 \sqrt{7} [/tex]
[tex]d) \sqrt{242} = \sqrt{2 \times 11 \times 11} = \sqrt{(11 \times 11) \times 2} = \sqrt{ {11}^{2} \times 2 } = 11 \sqrt{2} [/tex]
[tex]e) \sqrt{576} = \sqrt{ {24}^{2} } = 24 [/tex]
[tex]f) \sqrt{810} = \sqrt{2 \times 3 \times 3 \times 3 \times 3 \times 5} = \sqrt{(3 \times 3) \times (3 \times 3) \times 2 \times 5} = \sqrt{ {3}^{2} \times {3}^{2} \times 2 \times 5 } = (3 \times 3) \sqrt{2 \times 5} = 9 \sqrt{10} [/tex]
[tex]g) \sqrt{432} = \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3} = \sqrt{(2 \times 2) \times (2 \times 2) \times (3 \times 3) \times 3} = \sqrt{ {2}^{2} \times {2}^{2} \times {3}^{2} \times 3 } = (2 \times 2 \times 3) \sqrt{3} = 12 \sqrt{3} [/tex]
[tex]h) \sqrt{600} = \sqrt{2 \times 2 \times 2 \times 3 \times 5 \times 5} = \sqrt{(2 \times 2) \times (5 \times 5) \times 2 \times 3} = \sqrt{ {2}^{2} \times {5}^{2} \times 2 \times 3 } = (2 \times 5) \sqrt{2 \times 3} = 10 \sqrt{6} [/tex]
