Question

Equations and inequalities prior knowledge check

Answer 1

5⁹  is not a perfect Square

Step-by-step explanation:

To Check whether a number is  a perfect Square or not

we need to do the  prime factorization of number

if all prime factors are in even numbers  then  

number is a perfect Square Other wise not

Here given number = 1953125

= 5⁹

= 5 * 5 *5 *  5 * 5 * 5 * 5 * 5 * 5

Here Prime factor is only 5

and 5 is 9 times means odd times

hence 5⁹  is not a perfect Square

only being odd power Does not mean number is not a perfect Square

but odd power to prime number ensure that number is not a perfect Square

for example 9⁵   is a perfect square = (243)²

because 9 is not a prime number  

on prime factorization  9⁵   = (3 * 3)⁵ = (3²)⁵  =  3¹⁰  Which is even power

Hence number is Perfect Square

even 9⁹  is also a perfect square as = (3)¹⁸   ( even power)

5⁹  is not a perfect Square

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