Question

When $\sqrt[3]{2700}$ is simplified, the result is $a\sqrt[3]{b}$, where $a$ and $b$ are positive integers and $b$ is as small as possible. What is $a+b$?

Answer 1

103

Explanation:

To simplify
`\sqrt[3]{2700}`

`\sqrt[3]{2700}=\sqrt[3]{27X100}\\\\=\sqrt[3]{27}X\sqrt[3]{100}\\\\=3X\sqrt[3]{100}\\\\=3\sqrt[3]{100}`

Comparing our result with
`a\sqrt[3]{b}`

a=3, b=100

Therefore:

a+b=3+100=103