Question

Simplify the given expression.

square root of negative 6 end root times square root of negative 18

Answer 1

Simplify the given expression.

square root of negative 6 end root times square root of negative 18

Answer 2

Simplify the given expression.

square root of negative 108 end root plus square root of negative 27

Answer 3

Simplify the given expression.

square root negative 10 open parentheses 11 plus square root negative 5

Answer 4

anytime you deal with the square root of a negative number, you automatically introduce the imaginary number i, where \(\large i=\sqrt{-1} \).
let's try out the first problem and you try the others...

Answer 5

\[\huge \sqrt{-6}\cdot\sqrt{-18} \]
\[\huge =\sqrt{-1\cdot6}\cdot\sqrt{-1\cdot18} \]
\[\huge =\sqrt{-1}\cdot\sqrt{6}\cdot\sqrt{-1}\cdot\sqrt{18} \]
\[\huge =i\cdot\sqrt{2\cdot 3}\cdot i\cdot\sqrt{9\cdot 2} \]
\[\huge =i^2\cdot\sqrt{2}\sqrt{3}\cdot\sqrt{9}\cdot\sqrt{ 2} \]
\[\huge =(-1)\cdot 2\cdot\sqrt{3}\cdot3 \]
\[\huge =-6\sqrt{3} \]