Question

ME AYUDARIAN CON ESTO PLISS ES URGENTE ME TOCA ENTREGARLO ANTES DE AS 12 Y 15 DEL MEDIO DIA PORFI

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Answer 1

Hola!

Procedimiento paso a paso:

Te dejo la resolución de los ejercicios.

1)

a)

$\sqrt{245} = \sqrt{5 \times49} = \sqrt{5} \times \sqrt{49} = \sqrt{5} \times 7 = 7 \sqrt{5}$

b)

$\sqrt{450} = \sqrt{ 5 \times 90} = \sqrt{5 \times 5 \times 9 \times 2} = \sqrt{25 \times 9 \times 2} \\ = \sqrt{25} \times \sqrt{9} \times \sqrt{2} = 5 \times 3 \sqrt{2} = 15 \sqrt{2}$

c)

$\sqrt{432} = \sqrt{4 \times 108} = \sqrt{4 \times 27} = \sqrt{4 \times 9 \times 3} \\ = \sqrt{4} \times \sqrt{9} \times \sqrt{3} = 2 \times 9 \times \sqrt{3} = 18 \sqrt{3}$

d)

$\sqrt{900} = \sqrt{9 \times 100} = \sqrt{9} \times \sqrt{100} \\ = 3 \times \sqrt{10 \times 10} = 3 \sqrt{ {10}^{2} } = 3 \times 10 = 30$

2)

a)

$25(45 + 9 - 12 \div 3) - 15 + (18 \times 3 - 27 \times 2) + 1 \\ = 25(45 + 9 - (12 \div 3)) - 15 + ((18 \times 3) - (27 \times 2)) + 1 \\ = 25(45 + 9 - (4)) - 15 + ((54) - (54)) + 1 \\ = 25(45 + 9 - 4) - 15 + (54 - 54) + 1 \\ = 25(54 - 4) - 15 + (0) + 1 \\ = 25(50) - 15 + 1 \\ = 1250 - 15 + 1 \\ = 1235 + 1 \\ = 1236$

b)

$25 \times{96 - [960 \div 10(25 + 16 - 3 \times 5 - 125 \div 5)]} \\ 25 \times (96 - [960 \div 10(25 + 16 - 3 \times 5 - 125 \div 5)]) \\ 25 \times (96 - [(960 \div 10)(25 + 16 - (3 \times 5) - (125 \div 5)] )\\ 25 \times (96 - - [(96)(25 + 16 - 15 - 25)]) \\ 25 \times (96 - [(96)(25 - 25 + 16 - 15)] \\ 25 \times (96 - [(96)(1)]) \\ 25 \times (96 - [96]) \\ 25 \times (96 - 96) \\ 25 \times (0) \\ 0$

c)

$\sqrt{12 \times 5 + 10 \times 3 + 57 - 3} + {2}^{5} \\ = \sqrt{(12 \times 5) + (10 \times 3) + 57 - 3} + {2}^{5} \\ = \sqrt{(60) + (30) + 57 - 3} + 25 \\ = \sqrt{60 + 30 + 57 - 3} + 25 \\ = \sqrt{90 + 54} + 25 \\ = \sqrt{144} + 25 \\ = 12 + 25 \\ = 37$

d)

$\sqrt{ {2}^{5} \times {2}^{3} } \times {10}^{4} \div ( {4}^{2} \times {10}^{5} ) \\ = \sqrt{ {2}^{5 + 3} } \times {10}^{4} \div ( {( {2}^{2} )}^{2} \times {10}^{5} ) \\ = \sqrt{ {2}^{8}} \times {10}^{4} \div ( {2}^{4} \times {10}^{5} ) \\ = {2}^{ \frac{8}{2} } \times {10}^{4} \div ( {2}^{4} \times {10}^{5} ) \\ = {2}^{4} \times {10}^{4} \div ({2}^{4} \times {10}^{5} ) \\ = \frac{ {2}^{4} \times {10}^{4} }{({2}^{4} \times {10}^{5} ) } \\ = \frac{ {10}^{4} }{ {10}^{5} } \\ = {10}^{4 - 5} \\ = {10}^{ - 1} \\ = \frac{1}{10}$