Question

scoateți factorii de sub radical:
a)radical din 248
b)radical din 1260
c)radical din 1620
d)radical din 2250
e)radical din 5760
f)radical din 882
Vreau detaliat❤

Answer 1

$a) \sqrt{248} = \sqrt{2 \times 2 \times 2 \times 31} = \sqrt{(2 \times 2) \times 2 \times 31} = \sqrt{ {2}^{2} \times 2 \times 31 } = 2 \sqrt{2 \times 31} = 2 \sqrt{62}$

$b) \sqrt{1260} = \sqrt{2 \times 2 \times 3 \times 3 \times 5 \times 7} = \sqrt{(2 \times 2) \times (3 \times 3) \times 5 \times 7} = \sqrt{ {2}^{2} \times {3}^{2} \times 5 \times 7 } = (2 \times 3) \sqrt{5 \times 7} = 6 \sqrt{35}$

$c) \sqrt{1620} = \sqrt{2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 5} = \sqrt{(2 \times 2) \times (3 \times 3) \times (3 \times 3) \times 5} = \sqrt{ {2}^{2} \times {3}^{2} \times {3}^{2} \times 5 } = (2 \times 3 \times 3) \sqrt{5} = 18 \sqrt{5}$

$d) \sqrt{2250} = \sqrt{2 \times 3 \times 3 \times 5 \times 5 \times 5} = \sqrt{(3 \times 3) \times (5 \times 5) \times 2 \times 5} = \sqrt{ {3}^{2} \times {5}^{2} \times 2 \times 5 } = (3 \times 5) \sqrt{2 \times 5} = 15 \sqrt{10}$

$e) \sqrt{5760} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5} = \sqrt{(2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times 2 \times 5} = \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} \times {3}^{2} \times 2 \times 5 } = (2 \times 2 \times 2 \times 3) \sqrt{2 \times 5} = 24 \sqrt{10}$

$f) \sqrt{882} = \sqrt{2 \times 3 \times 3 \times 7 \times 7} = \sqrt{(3 \times 3) \times (7 \times 7) \times 2} = \sqrt{ {3}^{2} \times {7}^{2} \times 2 } = (3 \times 7) \sqrt{2} = 21 \sqrt{2}$