Question

multiply square root 2 (2+ square root 6)

Answer 1

Answer:

$\large\boxed{2\sqrt2+2\sqrt3}$

Step-by-step explanation:

$\sqrt2\cdot(2+\sqrt6)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(\sqrt2)(2)+(\sqrt2)(\sqrt6)\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=2\sqrt2+\sqrt{(2)(6)}\\\\=2\sqrt2+\sqrt{12}\\\\=2\sqrt2+\sqrt{(4)(3)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=2\sqrt2+\sqrt4\cdot\sqrt3\\\\=2\sqrt2+2\sqrt3$