Step-by-step explanation:
Given
[tex]1953125=5^9[/tex]
For a perfect square, its square root must be an integer
The square root of 1953125 i.e. [tex]\sqrt{1953125}=\sqrt{5^9}[/tex]
or, [tex]\sqrt{5^9}=5^\frac{9}{2}[/tex]
Clearly, [tex]\frac{9}{2}[/tex] is not an integer so, [tex]5^{\frac{9}{2}}[/tex] is also not an integer
Hence, 1953125 is not a square number
