Question

1 - Calcule as somas algébrica:
a)
$7 \sqrt[ 3]{10} + 3 \sqrt[3]{10} - 14 \sqrt[3]{10}$
b)
$5 + 7 \sqrt{5} + 3 \sqrt{5} - 2$
c)
$\sqrt{75} + \sqrt{ 12} - \sqrt{48}$
d)
$\sqrt{6} + 2 \sqrt{24} + \sqrt{54} - \sqrt{150}$


​

Answer 1

Resposta:

a) $-4\sqrt[3]{10}$

b) $3+10\sqrt{5}$

c) $3\sqrt{3}$

d) $3\sqrt{6}$

Explicação passo a passo:

1) a) $7\sqrt[3]{10} +3\sqrt[3]{10} -14\sqrt[3]{10}$

$(7 +3 -14)\sqrt[3]{10}$

$(10 -14)\sqrt[3]{10}$

$-4\sqrt[3]{10}$

b) $5+7\sqrt{5} +3\sqrt{5} -2$

$3+7\sqrt{5} +3\sqrt{5}$

$3+(7+3)\sqrt{5}$

$3+10\sqrt{5}$

c) $\sqrt{75} +\sqrt{12} -\sqrt{48}$

$\sqrt{25\times3 } +\sqrt{4\times3 } -\sqrt{16\times3 }$

$\sqrt{5^{2}\times3 } +\sqrt{2^{2}\times3 } -\sqrt{4^{2}\times3 }$

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

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

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

$(7-4)\sqrt{3}$

$3\sqrt{3}$

d) $\sqrt{6} +2\sqrt{24} +\sqrt{54} -\sqrt{150}$

$\sqrt{6} +2\sqrt{4\times6} +\sqrt{9\times6} -\sqrt{25\times6}$

$\sqrt{6} +2\sqrt{2^{2} \times6} +\sqrt{3^{2} \times6} -\sqrt{5^{2} \times6}$

$\sqrt{6} +2\sqrt{2^{2} }\sqrt{6} +\sqrt{3^{2} }\sqrt{6} -\sqrt{5^{2}}\sqrt{6}$

$\sqrt{6} +2\times2\sqrt{6} +3\sqrt{6} -5\sqrt{6}$

$\sqrt{6} +4\sqrt{6} +3\sqrt{6} -5\sqrt{6}$

$(1+4+3-5)\sqrt{6}$

$(5+3-5)\sqrt{6}$

$3\sqrt{6}$