if 0*0=0, why can’t you divide 0 by 0 (the square root of 0) and get 0 (the square root of 0)?

Question

ditto for cube root, nth root, etc.

In: 5

Answer 1

Think of multiplication as “taking from a box of apples” and division as “putting into a box of apples”.

Using those definitions, “0 * [any number]” is the same as “taking 0 apples from the box [any number] times”. At the end, how many apples do you have? Zero because you never actually took anything from the box.

For division, “[any number] divided by zero” is the same as “how many times can you put 0 apples into the box if you start with [any number]”. It’s obviously a pointless exercise so they call it “undefined”.