Question

Resolva a expressão e escreva a alternativa correta
$\sqrt{\frac{2^{28} +2^{30} }{10 } }$$a) \frac{2 ^{8} }{5} b) \frac{2 ^{9} }{5} c) 2^{8} d) 2^{9}$

Answer 1

$\sqrt{\dfrac{2^{28}+2^{30}}{10}}\\ \\ =\sqrt{\dfrac{2^{28}+2^{28+2}}{2 \cdot 5}}\\ \\ =\sqrt{\dfrac{2^{28}+2^{28}\cdot 2^{2}}{2 \cdot 5}}\\ \\ =\sqrt{\dfrac{2^{28}\cdot\left(1+2^{2} \right ) }{2 \cdot 5}}\\ \\ =\sqrt{\dfrac{2^{28}\cdot\left(1+4 \right ) }{2 \cdot 5}}\\ \\ =\sqrt{\dfrac{2^{28}\cdot \diagup\!\!\!\!5}{2 \cdot \diagup\!\!\!\!5}}\\ \\ =\sqrt{\dfrac{2^{28}}{2^{1}}}\\ \\ =\sqrt{2^{28-1}}\\ \\ =\sqrt{2^{27}}$


Nenhuma das alternativas.