Question

1) Simplifique os radicais e efetue as operações:
a) √2 + √32= 5√2
b) √27 + √3 = 4√3
c) 3√5 + √20 = 5√5
d) 2√2 + √8 = 4√2
e) √27 + 5√3
f) 2√7 + √28 = 4√7
g) √50 - √98 = -2√2
h) √12 - 6√3 = -4√3
i) √20 - √45 = -√5

Answer 1

a)

$\sqrt{2} + \sqrt{32} + 5 \sqrt{2} = \sqrt{2} + \sqrt{2 {}^{2} } + \sqrt{2 {}^{2} } + 2 = 5 \sqrt{2} = \sqrt{2} + 2 \times 2 \sqrt{2} + 5 \sqrt{2} = \sqrt{2} + 4 \sqrt{2} + 5 \sqrt{2} = 10 \sqrt{2}$

b)

$\sqrt{3 {}^{2} } + 3 + \sqrt{3} + 4 \sqrt{3} = 3 \sqrt{3} + \sqrt{3} + 4 \sqrt{3} = 8 \sqrt{3}$

c)

$3 \sqrt{5} + \sqrt{} 2 {}^{2} + 5 + 5 \sqrt{5} = 3 \sqrt{5} + 2 \sqrt{5} + 5 \sqrt{5} = 10 \sqrt{5}$

d)

$2 \sqrt{2} +4 \sqrt{2} + \sqrt{2 {}^{2} } + 2 = 2 \sqrt{2} + 4 \sqrt{2} + 2 \sqrt{2} = 8 \sqrt{2}$

e)

$5 \sqrt{3} + \sqrt{3 {}^{2} } + 3 = 5 \sqrt{3} + 3 \sqrt{3} = 8 \sqrt{3}$

f)

$2 \sqrt{7} + 4 \sqrt{7} + \sqrt{28} = 2 \sqrt{7} + 4 \sqrt{7} + \sqrt{2 {}^{2} } + 7 = 2 \sqrt{7} + 2 \sqrt{7} + 4 \sqrt{7} = 8 \sqrt{7}$

g)

$\sqrt{5 {}^{2} } + 2 - \sqrt{7 ^{2} } + 2 - ( - 2 \sqrt{7)} = 5 \sqrt{2} - 7 \sqrt{2} - ( - 2 \sqrt{7)} = 0 \sqrt{7}$

h)

$\sqrt{2 {}^{2} } + 3 - 6 \sqrt{3} - 4 \sqrt{3} = 2 \sqrt{3} + 6 \sqrt{3} - 4 \sqrt{3} = 4 \sqrt{3}$

i)

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