Question

26. Escreva as expressões abaixo de maneira
simplificada
a) V50 + V32 - V18
b)2V3+ 27 + V75
c)3816 + 754 - 3V128
d) V 375 + 24 + V192 - 1648
e) 2V18 - 6V288 + V1800
f)2V80 - V45 + V245
00
g) V162 - V1250 - 2592​

Answer 1

Oie, Td Bom?!

a)

$= \sqrt{50} + \sqrt{32} - \sqrt{18}$

$= \sqrt{5 {}^{2} \: . \: 2} + \sqrt{4 {}^{2} \: . \: 2} - \sqrt{3 {}^{2} \: . \: 2 }$

$= \sqrt{5 {}^{2} } \sqrt{2} + \sqrt{4 {}^{2} } \sqrt{2} - \sqrt{3 {}^{2} } \sqrt{2}$

$= 5 \sqrt{2} + 4 \sqrt{2} - 3 \sqrt{2}$

$= (5 + 4 - 3) \sqrt{2}$

$= 6 \sqrt{5}$

b)

$= 2 \sqrt{3} + 27 + \sqrt{75}$

$= 2 \sqrt{3} + 27 + \sqrt{5 {}^{2} \: . \: 3 }$

$= 2 \sqrt{3} + 27 + \sqrt{5 {}^{2} } \sqrt{3}$

$= 2 \sqrt{3} + 27 + 5 \sqrt{3}$

$= (2 + 5) \sqrt{3} + 27$

$= 7 \sqrt{3} + 27$

c)

$= 3816 + 754 - 3 \sqrt{128}$

$= 4570 - 3 \sqrt{8 {}^{2} \: . \: 2}$

$= 4570 - 3 \sqrt{8 {}^{2} } \sqrt{2}$

$= 4570 - 3 \: . \: 8 \sqrt{2}$

$= 4570 - 24 \sqrt{2}$

d)

$= \sqrt{375} + 24 + \sqrt{192} - 1648$

$= \sqrt{5 {}^{2} \: . \: 15} + 24 + \sqrt{8 {}^{2} \: . \: 3} - 1648$

$= \sqrt{5 {}^{2} } \sqrt{15} + 24 + \sqrt{8 {}^{2} } \sqrt{3} - 1648$

$= 5 \sqrt{15} - 1624 + 8 \sqrt{3}$

e)

$= 2 \sqrt{18} - 6 \sqrt{288} + \sqrt{1800}$

$= 2 \sqrt{3 {}^{2} \: . \: 2 } - 6 \sqrt{12 {}^{2} \: . \: 2} + \sqrt{30 {}^{2} \: . \: 2}$

$= 2 \: . \: \sqrt{3{}^{2} } \sqrt{2} - 6 \sqrt{12 {}^{2} } \sqrt{2} + \sqrt{30 {}^{2} } \sqrt{2}$

$= 2 \: . \: 3 \sqrt{2} - 6 \: . \: 12 \sqrt{2} + 30 \sqrt{2}$

$= 6 \sqrt{2} - 72 \sqrt{2} + 30 \sqrt{2}$

$= (6 - 72 + 30) \sqrt{2}$

$= - 36 \sqrt{2}$

f)

$= 2 \sqrt{80} - \sqrt{45} + \sqrt{245}$

$= 2 \sqrt{4 {}^{2} \: . \: 5} - \sqrt{3 {}^{2} \: . \: 5} + \sqrt{7 {}^{2} \: . \: 5 }$

$= 2 \sqrt{4 {}^{2} } \sqrt{5} - \sqrt{3 {}^{2} } \sqrt{5} + \sqrt{7 {}^{2} } \sqrt{5}$

$= 2 \: . \: 4 \sqrt{5} - 3 \sqrt{5} + 7 \sqrt{5}$

$= 8 \sqrt{2} - 3 \sqrt{5} + 7 \sqrt{5}$

$= (8 - 3 + 7) \sqrt{5}$

$= 12 \sqrt{5}$

g)

$= \sqrt{162} - \sqrt{1250} - 2592$

$= \sqrt{9 {}^{2} \: . \: 2 } - \sqrt{25 {}^{2} \: . \: 2} - 2592$

$= \sqrt{9 {}^{2} } \sqrt{2} - \sqrt{25 {}^{2} } \sqrt{2} - 2592$

$= 9 \sqrt{2} - 25 \sqrt{2} - 2592$

$= (9 - 25) \sqrt{2} - 2592$

$= - 16 \sqrt{2}$

Att. Makaveli1996