I have simple multiplication confusion, any help would be great

Question

$(\mathbf60\times\mathbf60)$ Seconds = $3600$ Seconds or $60$ Minutes

while

$(1\times 1)$ Minute = 1 Minute

What am I missing? and sorry about formatting i am new here on math network

Answer 1

The problem here is units.

The result of multiplying 60 seconds by 60 seconds isn't in seconds: it is in $\sec^2$. Similarly, the result of multiplying 1 minute by 1 minute isn't in terms of minutes, it is in terms of $\min^2$.

The kicker, then, is that $$ 1\text{min}^2=(1\text{min})(1\text{min})=(60\text{sec})(60\text{sec})=3600\text{sec}^2. $$