Question

Resolva as raizes:
a) √200 + √300
b) √500 + √162
c) √600 + √216
d) √162 + √250
e) √512 + √2048

Alguém me ajuda por favor eu preciso com cálculos!❤​

Answer 1

Explicação passo-a-passo:

a)

$\sqrt{200} + \sqrt{300} = \sqrt{100.2} + \sqrt{100.3} = 10 \sqrt{2} + 10 \sqrt{3} = 10( \sqrt{2} + \sqrt{3} )$

b)

$\sqrt{500} + \sqrt{162} = \sqrt{100.5} + \sqrt{81.2} = 10 \sqrt{5} + 9 \sqrt{2}$

c)

$\sqrt{600} + \sqrt{216} = \sqrt{100.6} + \sqrt{ {2}^{3}. {3}^{3} } = 10 \sqrt{6} + \sqrt{ {2}^{2}.2. {3}^{2}.3 } = 10 \sqrt{6} + 2.3 \sqrt{2.3} = 10 \sqrt{6} + 6 \sqrt{6} = 16 \sqrt{6}$

d)

$\sqrt{162} + \sqrt{250} = \sqrt{81.2} + \sqrt{25.10} = 9 \sqrt{2} + 5 \sqrt{10}$

e)

$\sqrt{512} + \sqrt{2048} = \sqrt{ {2}^{9} } + \sqrt{ {2}^{11} } = \sqrt{ {2}^{8}.2} + \sqrt{ {2}^{10}.2} = {2}^{4}. \sqrt{2} + {2}^{5}. \sqrt{2} = 16 \sqrt{2} + 32 \sqrt{2} = 48 \sqrt{2}$