Find the value of the following expression: 4sqrt2+2(sqrt36-sqrt8)

Irrational numbers
Find the value of the following expression:
$$\displaystyle{4}\sqrt{{2}}+{2}{\left(\sqrt{{36}}-\sqrt{{8}}\right)}$$

2021-02-22
$$\displaystyle{4}\sqrt{{2}}+{2}{\left(\sqrt{{36}}-\sqrt{{8}}\right)}={4}\sqrt{{2}}+{2}{\left({6}-\sqrt{{{4}\times{2}}}\right)}$$
$$\displaystyle={4}\sqrt{{2}}+{12}-{4}\sqrt{{2}}$$
$$\displaystyle={\left({4}\sqrt{{2}}-{4}\sqrt{{2}}\right)}+{12}$$
=0+12
=12
$$\displaystyle{4}\sqrt{{2}}+{2}{\left(\sqrt{{36}}-\sqrt{{8}}\right)}={12}$$