Đáp án:
$\dfrac{-12+12\sqrt[]{6}}{5}$
Giải thích các bước giải:
$\dfrac{12}{\sqrt[]{7+\sqrt[]{24}}}$
$=\dfrac{12}{\sqrt[]{7+\sqrt[]{2^2.6}}}$
$=\dfrac{12}{\sqrt[]{7+2\sqrt[]{6}}}$
$=\dfrac{12}{\sqrt[]{(\sqrt[]{6}+1)^2}}$
$=\frac{12}{|\sqrt[]{6}+1|}$
$=\frac{12}{\sqrt[]{6}+1}$
$=\dfrac{12(\sqrt[]{6}-1)}{(\sqrt[]{6}+1)(\sqrt[]{6}-1)}$
$=\dfrac{-12+12\sqrt[]{6}}{5}$