Question

Simplify the given expression.

square root of negative 10 end root times square root of negative 8

Answer 1

negative 4 square root 5
4 square root of 5
4 I square root of 5
negative 4 I square root of 5

Answer 2

i got the 3rd one is it right?

Answer 3

i∗10−−√∗8√∗i

−80−−√=−45√

Answer 4

\[\large \sqrt{-10}*\sqrt{-8}\]
\[\large \sqrt{-1*10}*\sqrt{-1*8}\]
\[\large \sqrt{-1}*\sqrt{10}*\sqrt{-1}*\sqrt{8}\]
\[\large \sqrt{-1}*\sqrt{-1}*\sqrt{10}*\sqrt{8}\]
\[\large i*i*\sqrt{10}*\sqrt{8}\]
\[\large i^2*\sqrt{10}*\sqrt{8}\]
\[\large -1*\sqrt{10}*\sqrt{8}\]

I'll let you finish up.

Answer 5

\(\bf \sqrt{-10}\cdot \sqrt{-8}\implies \sqrt{10\cdot -1}\cdot \sqrt{8\cdot -1}\implies \sqrt{10}\cdot \sqrt{-1}\cdot \sqrt{8}\cdot \sqrt{-1}
\\ \quad \\
\sqrt{10}\ i\cdot \sqrt{8}\ i\implies \sqrt{10\cdot 8}\ i \cdot i\implies \sqrt{80}\ i^2\implies \sqrt{4^2\cdot 5}\ i^2
\\ \quad \\
{\color{brown}{ i^2\to \sqrt{-1}\cdot \sqrt{-1}\to \sqrt{(-1)^2}\to -1}}
\\ \quad \\
-1\cdot \sqrt{4^2\cdot 5}\implies -4\sqrt{5}\)