Question

given that 23×52×11×n, where n is a whole number.what is the smallest value of n that will make this number into a perfect square ? ​

Answer 1

Answer:

Given: 23×52×11×n.What is the smallest value of n that will make this number into a perfect square?

A number is a perfect square if and only if the powers in the prime factorization are even. So lets first look at:

23⋅52⋅11

Now split every composite number into multiplications of prime numbers.

=23⋅(22⋅13)⋅11=22⋅11⋅13⋅23 (23 and 11 are already prime numbers)

Now n has to add a factor of 23, a factor of 13 and a factor of 11, to only have even powers in the prime factorization, so now we know:

n=23⋅13⋅11=2389 , that’s the smallest answer. It is the smallest answer, because every power in the prime factorization is even and the smallest even number possible. But only if 0 isn’t an answer.

Please ask for a proof if you would like to see why the powers in the prime factorization have to be even to get an integer answer.

Step-by-step explanation:

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Answer 2

Answer:

0 is answer

Step-by-step explanation:

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