Assuming initially √(-14√-98)=
√(-7√-196)=√(-7√-14²)=
√(-7×14i) where i is the imaginary square root of -1.
This is √-98i.
Let √i=a+ib, then i=a²-b²+2abi, so, equating complex components, a²=b²⇒a=b, and 2ab=2a²=1, a=√2/2.
√i=(√2/2)(1+i).
√98=7√2, so √-98i=(√-98)(√i)=
(7i√2)(√2/2)(1+i)=
(7i)(1+i)=7(i-1).
If you meant (√-14)(√-98), then:
(i√14)(7i√2)=-7√28=-7√(4×7)=-14√7.
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