Answer:
[tex]\large\boxed{10.1\ cm}[/tex]
Step-by-step explanation:
The formula of a volume of a cube:
[tex]V=a^2[/tex]
a - length of the edge
We have a = 8cm. Substitute:
[tex]V=8^3=512\ cm^3[/tex]
The volume of second cube:
[tex]V'=2V\to V'=2(512\ cm^3)=1024\ cm^3[/tex]
The length of the edge of the second cube (b):
[tex]b^3=1024\to b=\sqrt[3]{1024}\ cm^3[/tex]
[tex]1024=2^{10}=2^{9+1}=2^9\cdot2[/tex]
Used [tex]a^n\cdot a^m=a^{n+m}[/tex]
[tex]b=\sqrt[3]{1024}=\sqrt[3]{2^{10}}=\sqrt[3]{2^9\cdot2}=\sqrt[3]{2^9}\cdot\sqrt[3]{2}[/tex]
Use [tex](a^n)^m=a^{nm}[/tex]
[tex]=\sqrt[3]{2^{3\cdot3}}\cdot\sqrt[3]{2}=\sqrt[3]{(2^3)^3}\cdot\sqrt[3]{2}[/tex]
Use [tex]\sqrt[3]{a^3}=a[/tex]
[tex]=2^3\sqrt[3]{2}=8\sqrt[3]{2}\ cm[/tex]
[tex]\sqrt[3]{2}\approx1.26\to b\approx8(1.26)\approx10.1\ cm[/tex]
Other method:
[tex]V'=2V\\\\V=a^3,\ V'=b^3\to b^3=2a^3\to b=\sqrt[3]{2a^3}\\\\b=a\sqrt[3]2[/tex]
[tex]a=8\ cm\to b=8\sqrt[3]2\ cm\approx10.1\ cm[/tex]
