Question

What are the fourth rots of 64?

Answer 1

`\sqrt[4]{64}`≈2,8284...

Explanation:

We have to calculate
`\sqrt[4]{64}`, first we have to factor 64.

`64 |\\32| 2\\16|2\\8|2\\4|2\\2|2\\1|2\\`

Then we can write 64 as:

`64=2*2*2*2*2*2=2^4*2^2`

`\sqrt[4]{64}=\sqrt[4]{2^4*2^2}=\sqrt[4]{2^4} *\sqrt[4]{2^2} =2*\sqrt[4]{2^2}`

We can rewrite
`\sqrt[4]{2^2}=\sqrt{√(2^2)}`,then

`\sqrt[4]{64}=2*\sqrt{√(2^2)}=2√(2)`

The result is:

`\sqrt[4]{64}=2√(2)`≈2,8284...