Question

Identify all of the real fifth roots of 1024.

Answer 1

Answer:

Real fifth root of 1024 is 4.

Step-by-step 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.

Answer 2

Answer:

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

Step-by-step explanation:

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