Question

Write the given surd $\sqrt[4]{45000}$ in its simplest form

Answer 1

To simplify $\sqrt[4]{4500}$ we may proceed as follows by splitting the number into its prime factors.

$\sqrt[4]{4500}$ $=$ $\sqrt[4]{42\times 2\times 2\times 5\times 5\times 5\times 5}$

$=$ $\sqrt[4]{45\times 5\times 5\times 5}$ $\times$$\sqrt[4]{42\times 2\times 2}$

$=$ $5$$\sqrt[4]{42\times 2\times 2}$

$=$ $5$$\sqrt[4]{48}$