Answer:
[tex]\huge\boxed{\sqrt{10+4\sqrt6}=\sqrt6+2}[/tex]
Step-by-step explanation:
[tex]\sqrt{10+4\sqrt6}=\sqrt{6+4+(2)(2)(\sqrt6)}=\sqrt{\underbrace{(\sqrt6)^2}_{=6}+(2)(2)(\sqrt6)+\underbrace{2^2}_{=4}}\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=\sqrt{(\sqrt6+2)^2}\\\\\text{use}\ \sqrt{a^2}=|a|\\\\=|\sqrt6+2|=\sqrt6+2[/tex]
