Question

Simplify (square root 2)( square root of 2^3)

Answer 1

`\large\boxed{(\sqrt2)(√(2^3))=4}`

Explanation:

`(\sqrt2)(√(2^3))\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=√(2\cdot2^3)\qquad\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=\sqrt{2^(1+3)}=√(2^4)\\\\(1)=\sqrt{2^(2\cdot2)}\qquad\text{use}\ (a^n)^m=a^(nm)\\\\=√((2^2)^2)\qquad\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=2^2=4\\\\(2)=√(2\cdot2\cdot2\cdot2)=√(16)=6\ \text{because}\ 4^2=16`