Question

find the smallest value of n such that 164n is a perfect square.​

Answer 1

Answer:

41

Step-by-step explanation:

Prime Factorisation:

164 = 2 x 2 x 41

We can see that "2" has a pair , while "41" does not.

So the value of "n' must be 41 , to make 164 a Perfect square.

If 41 is multiplied to 164 , then 41 will also have a pair of no: , when the square root is taken only one no: from each pair is taken.

Hence, when 'n = 41' , 164n will be a perfect square.

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