what's the geometric mean of 31 and 42? do I just multiply them and then square root?

Question

jim_thompson5910 · Answer

you are absolutely correct

anonymous · Answer

after i multiply them my teacher told us to find two #'s that you can multiply and get that product, but one of those has to be a perfect square :( so i'm stuck at 1302 because what number can i multiply to get that but one has to be a perfect square ....

jim_thompson5910 · Answer

try listing the list of perfect squares

1, 4, 9, 16, 25, 36, ...

and see which number is a factor of 1302

jim_thompson5910 · Answer

it turns out that 1302 has no such factors

we can prove this by looking at the prime factorization of 1302

jim_thompson5910 · Answer

1302 = 31*42

1302 = 31*6*7

1302 = 31*2*3*7

Notice we have no repeat factors. So that means there are no perfect square factors

anonymous · Answer

I will leave it as that then, thank you! :)

jim_thompson5910 · Answer

you're welcome