A DESCRIPTION OF THE PROBLEM :
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jshell> BigInteger b = BigInteger.valueOf(Long.MAX_VALUE);
b ==> 9223372036854775807

jshell> b.sqrt();
$2 ==> 3037000499

jshell> 3037000499L*3037000499L
$3 ==> 9223372030926249001

jshell> 9223372036854775807L-9223372030926249001L
$4 ==> 5928526806

jshell> BigInteger c = b.sqrt();
c ==> 3037000499

jshell> c.pow(2);
$6 ==> 9223372030926249001

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
As with smaller integers:

jshell> BigInteger b = BigInteger.valueOf(16);
b ==> 16

jshell> b.sqrt();
$9 ==> 4

jshell> 4*4
$10 ==> 16

jshell> BigInteger c = b.sqrt();
c ==> 4

jshell> c.pow(2);
$12 ==> 16