Question

how to simplify surds 5th√2048​

Answer 1

Answer:

$\sqrt[5]{2048}$ $= 4\sqrt[5]{2}$

Step-by-step explanation:

2048

= 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2. 2 . 2

$= 2 . 2^{10}$

Therefore, $\sqrt[5]{2048}$

$= (2 . 2^{10} )^\frac{1}{5}$

$= (2^{\frac{1}{5}} . 2^{\frac{10}{5} } )$

$= 2^2 . \sqrt[5]{2}$

$= 4\sqrt[5]{2}$