Question

Identify all of the real fifth roots of 1024.

Answer 1

`\large\boxed{\sqrt[5]{1024}=4}`

Explanation:

`\begin{array}c1024&2\\512&2\\256&2\\128&2\\64&2\\32&2\\16&2\\8&2\\4&2\\2&2\\1\end{array}\\\\1024=\underbrace{2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2}_(10)=2^(10)\\\\\sqrt[5]{1024}=\sqrt[5]{2^(10)}\\\\\text{Use}\ (a^n)^m=a^(nm)\\\\=\sqrt[5]{2^(2\cdot5)}=\sqrt[5]{(2^2)^5}=\sqrt[5]{4^5}\\\\\text{Use}\ \sqrt[n]{a^n}=a\\\\=\boxed4`

Answer 2

Real fifth root of 1024 is 4.

Explanation:

We have to find the value of real fifth root of 1024.

For this let fifth root of 1024 = x

Therefore
`x^(5) = 1024 = 4^(5)`

Or
`x^(5)=4^(5)`

Therefore x = 4

X= 4 is the right answer.