Question

Simplifique as expressões​

Answer 1

Explicação passo-a-passo:

A)

$\sqrt{54} + \sqrt{486} - \sqrt{294}$

$\sqrt{3 {}^{2} \times 6 } + \sqrt{9 {}^{2} \times 6 } - \sqrt{7 {}^{2} \times 6}$

$\sqrt{3 {}^{2} } \sqrt{6} + \sqrt{9 {}^{2} } \sqrt{6} + \sqrt{7 {}^{2} } \sqrt{6}$

$3 \sqrt{6} + 9 \sqrt{6} - 7 \sqrt{6}$

$(3 + 9 - 7) \sqrt{6}$

=>5√6

B)

$\sqrt{128} - \sqrt{98} + \sqrt{242}$

$2 {}^{3} \sqrt{2} - \sqrt{7 {}^{2} \times 2} + \sqrt{11 {}^{2} \times 2 }$

$8 \sqrt{2} - \sqrt{7 {}^{2} } \sqrt{2} + \sqrt{11 {}^{2} } \sqrt{2}$

$8 \sqrt{2} - 7 \sqrt{2} + 11 \sqrt{2}$

$(8 - 7 + 11) \sqrt{2}$

=>12√2

C)

$\sqrt[3]{189} + \sqrt[3]{448} + \sqrt[3]{875}$

$\sqrt[3]{3 {}^{3} \times 7 } + \sqrt[3]{4 {}^{ 3} \times 7 } + \sqrt[3]{5 {}^{3} \times 7 }$

$\sqrt[3]{3 {}^{3} } \sqrt[3]{7} + \sqrt[3]{4 {}^{3} } \sqrt[3]{7} + \sqrt[3]{5 {}^{3} } \sqrt[3]{7}$

$3 \sqrt[3]{7} + 4 \sqrt[3]{7} + 5 \sqrt[3]{7}$

$(3 + 4 + 5) \sqrt[3]{7}$

=>12³√7

D)

$\sqrt{396} + \sqrt{108} + \sqrt{176} - \sqrt{675}$

$\sqrt{6 {}^{2} \times 11 } + \sqrt{6 {}^{2} \times 3 } + \sqrt{4 {}^{2} \times 11 } + \sqrt{15 {}^{2} \times 3}$

$\sqrt{6 {}^{2} } \sqrt{11} + \sqrt{6 {}^{2} } \sqrt{3} + \sqrt{4 {}^{2} } \sqrt{11} - \sqrt{15 {}^{2} } \sqrt{3}$

$6 \sqrt{11} + 6 \sqrt{3 } + 4 \sqrt{11} - 15 \sqrt{3}$

$(6 + 4) \sqrt{11} + ( 6 - 15) \sqrt{3}$

$10 \sqrt{11} + ( - 9) \sqrt{3}$

=>10√11-9√3