Answer:
[tex]\sqrt[4]{64}[/tex]≈2,8284...
Step-by-step explanation:
We have to calculate [tex]\sqrt[4]{64}[/tex], first we have to factor 64.
[tex]64 |\\32| 2\\16|2\\8|2\\4|2\\2|2\\1|2\\[/tex]
Then we can write 64 as:
[tex]64=2*2*2*2*2*2=2^4*2^2[/tex]
[tex]\sqrt[4]{64}=\sqrt[4]{2^4*2^2}=\sqrt[4]{2^4} *\sqrt[4]{2^2} =2*\sqrt[4]{2^2}[/tex]
We can rewrite [tex]\sqrt[4]{2^2}=\sqrt{\sqrt{2^2}}[/tex],then
[tex]\sqrt[4]{64}=2*\sqrt{\sqrt{2^2}}=2\sqrt{2}[/tex]
The result is:
[tex]\sqrt[4]{64}=2\sqrt{2}[/tex]≈2,8284...
