Question

1. write the expression in simplest form. write your answer as a radical expression.

$sqrt5{288} = \square$

Explanation:

Step1: Prime factorize 288

$$288 = 2^5\times3^2$$

Step2: Apply the property of radicals \(\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\)

$$\sqrt[5]{288}=\sqrt[5]{2^5\times3^2}$$

Step3: Simplify using \(\sqrt[5]{a^5}=a\)

$$\sqrt[5]{2^5\times3^2}=2\sqrt[5]{3^2}$$

Step4: Calculate \(3^2\)

$$2\sqrt[5]{3^2}=2\sqrt[5]{9}$$

Answer:

\(2\sqrt[5]{9}\)