Question

scoaterea factorilor de sub radical. calculati: √450 ; √216 ; √343 ; √242 ; √576 ; √810 ; √432 ; √600 va rog e pt maine am foarte multe teme multumesc

Answer 1

$a)\sqrt{450} = \sqrt{2 \times 3 \times 3 \times 5 \times 5} = \sqrt{(3 \times 3) \times (5 \times 5) \times 2} = \sqrt{ {3}^{2} \times {5}^{2} - 2 } = (3 \times 5) \sqrt{2} = 15 \sqrt{2}$

$b) \sqrt{216} = \sqrt{2 \times 2 \times 2 \times 3 \times 3 \times 3} = \sqrt{(2 \times 2) \times (3 \times 3) \times 2 \times 3} = \sqrt{ {2}^{2} \times {3}^{2} \times 2 \times 3 } = (2 \times 3) \sqrt{2 \times 3} = 6 \sqrt{6}$

$c) \sqrt{343} = \sqrt{7 \times 7 \times 7} = \sqrt{(7 \times 7) \times 7} = \sqrt{ {7}^{2} \times 7 } = 7 \sqrt{7}$

$d) \sqrt{242} = \sqrt{2 \times 11 \times 11} = \sqrt{(11 \times 11) \times 2} = \sqrt{ {11}^{2} \times 2 } = 11 \sqrt{2}$

$e) \sqrt{576} = \sqrt{ {24}^{2} } = 24$

$f) \sqrt{810} = \sqrt{2 \times 3 \times 3 \times 3 \times 3 \times 5} = \sqrt{(3 \times 3) \times (3 \times 3) \times 2 \times 5} = \sqrt{ {3}^{2} \times {3}^{2} \times 2 \times 5 } = (3 \times 3) \sqrt{2 \times 5} = 9 \sqrt{10}$

$g) \sqrt{432} = \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3} = \sqrt{(2 \times 2) \times (2 \times 2) \times (3 \times 3) \times 3} = \sqrt{ {2}^{2} \times {2}^{2} \times {3}^{2} \times 3 } = (2 \times 2 \times 3) \sqrt{3} = 12 \sqrt{3}$

$h) \sqrt{600} = \sqrt{2 \times 2 \times 2 \times 3 \times 5 \times 5} = \sqrt{(2 \times 2) \times (5 \times 5) \times 2 \times 3} = \sqrt{ {2}^{2} \times {5}^{2} \times 2 \times 3 } = (2 \times 5) \sqrt{2 \times 3} = 10 \sqrt{6}$