Question

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

Answer 1

Answer:

$\large\boxed{(\sqrt2)(\sqrt{2^3})=4}$

Step-by-step explanation:

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