Roots of perfect numbers

Algebra Level 2

Let $P_{n}$ to the $n$ th perfect number.

Then what is the largest number of $\displaystyle \sqrt { P_{n} }$ ?

\sqrt { 8128 }

\sqrt { 28 }

. Cannot be counted.

\sqrt { 6 }

\sqrt { 496 }

\sqrt { 33550336 }

\sqrt { 8589869056 }

\sqrt { 137438691328 }

1 solution

. .
Feb 16, 2021

The largest perfect number that $P_{n}$ is not found, so there is no square root of $P_{n}$ that $\sqrt { P_{n} }$ .