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### is $\sqrt{n!}\notin\mathbb{Z}$ for $n>1$ true? [duplicate]

Is it true that $\sqrt{n!}\notin\mathbb{Z}$ for $n>1$? This is what I did: By induction: for $n=2$ its trivial ($\sqrt{2}$ is irrational). Suppose its true for some $n\in\mathbb{N}$, then the ...
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### Is there any number which is a perfect square of some number as well as factorial of some number. [duplicate]

Is there any number which is a perfect square of some number as well as factorial of some number? That is, let x be such a number, then x can be expressed as ...
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### Is $\sqrt{n!}$ a natural number?

I'm new here (on Mathematics Stack Exchange). Also, I'm a 10th grade student not a math expert. So, my question is whether, $$\sqrt {n!}$$ comes in the set of the Natural Numbers. There were ...
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### Factorials and their perfect squares

How many positive factorials are also perfect Squares. So for example $1!=1=1^2$. How many others exist other than 1? Is there any way to prove this?
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### Prove: $\lfloor \sqrt{n!}\rfloor\nmid n!$ [closed]

$n$ is an integer greater than $7$. How does one go about proving that $\lfloor \sqrt{n!}\rfloor\nmid n!$.
### Prove that $L_1$ = $\{1^m :$ m is not a perfect square$\}$ is not regular using Pumping Lemma
I'm trying to prove that the Language $L_1$ = $\{1^m :$ m is not a perfect square$\}$ is not regular. I proved before that L = $\{1^m :$ m is a perfect square$\}$ is not regular, I thought that I ...
### Occurrence (parity) of primes in $n!$
It is known that $n!$ can not be a perfect square for $n\geq 1$. This means that in the prime decomposition of $n!$, one of the prime occurs odd number of times. This leads to following two questions: ...