Square Root of $320$

Question

Given, $$\sqrt{5} = 2.236$$ $$\sqrt{320} = 2^3 \times \sqrt{5} = 8 \times 2.236 = 17.888$$

This is the explanation provided in my school book. Could someone please elaborate ?
Thanks in advance.

Answer 1

It uses three facts: that $\sqrt{a}=a^{1/2}$ and $(a^b)^c=a^{bc}$ and $(ab)^c=a^cb^c$.

$320 = 32 \times 10 = 2\times2\times2\times2\times2\times2\times5=2^6\times5$. So $(2^65)^{1/2}=2^35^{1/2}$.

Answer 2

$320=64\cdot 5=2^6\cdot 5$ Then $\sqrt{320}=\sqrt{2^6\cdot 5}=\sqrt{2^6}\cdot \sqrt{5}=2^3\cdot \sqrt{5}$