Question

Please show steps!1​

Answer 1

Answer:

$5\sqrt[3]{25}$

Step-by-step explanation:

Let's factor to see if it's a perfect cube: 3 is a factor, so let's divide: $1875:3 = 625$. 625 is no longer divisible by 3, but it is by 5, in particular it's $5^4 = 625$. At this point we can start taking out of the cube root as much as we can:

$\sqrt[3]{1875} = \sqrt[3]{3\times 5^4} = \sqrt[3]{3\times 5\times 5^3} = 5 \sqrt[3]{3\times5} = 5\sqrt[3]{25}$