Đáp án:
$4$
Giải thích các bước giải:
$\sqrt[3]{20+14\sqrt[]{2}}+\sqrt[3]{20-14\sqrt[]{2}}$
$=\sqrt[3]{8+12+12\sqrt[]{2}+2\sqrt[]{2}}+\sqrt[3]{8+12-12\sqrt[]{2}-2\sqrt[]{2}}$
$=\sqrt[3]{2^3+3.2^2.\sqrt[]{2}+3.2.(\sqrt[]{2})^2+(\sqrt[]{2})^3}+\sqrt[3]{2^3-3.2^2.\sqrt[]{2}+3.2.(\sqrt[]{2})^2-(\sqrt[]{2})^3}$
$=\sqrt[3]{(2+\sqrt[]{2})^3}+\sqrt[3]{(2-\sqrt[]{2})^3}$
$=2+\sqrt[]{2}+2-\sqrt[]{2}$
$=4$
