Question

Zarea finds 3^√6000 and shows her work below. 3^√6000 = 3^√? x 3^√6 = 10 ^3√6 what is the missing value?

Answer 1

? = 1000

Explanation:

Zarea is making use of the fact that the cube root of a product is the product of the cube roots. She is factoring out the largest perfect cube in the number 6000.

`\displaystyle \sqrt[3]{6000}=\sqrt[3]{1000\cdot6}=\sqrt[3]{\boxed{1000}}\cdot\sqrt[3]{6}=10\sqrt[3]{6}`

The missing value in Zarea's work is 1000.