If $x=735$ and $ax$ is a perfect square where $a$ is a positive integer, what is the smallest possible value of $\sqrt{ax}$?
+364 x=735
735a=perfect square
well, 735=7×105=7×5×3×7
735=3×5×72
in order to get a perfect square, you will need a 3 and a 5 because every number in the prime factorization needs to have a square.
√735⋅15=√32⋅52⋅72=3⋅5⋅7=105
notice that you can take a shortcut by multiplying 3x5x7.
I'll let you wonder why, but it works all the time!
+364 x=735
735a=perfect square
well, 735=7×105=7×5×3×7
735=3×5×72
in order to get a perfect square, you will need a 3 and a 5 because every number in the prime factorization needs to have a square.
√735⋅15=√32⋅52⋅72=3⋅5⋅7=105
notice that you can take a shortcut by multiplying 3x5x7.
I'll let you wonder why, but it works all the time!
