Question

Multiply square root 2 (2+ square root 6)

Answer 1

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

Explanation:

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