Question

HELP THIS IS DUE TODAY
(-9-√-32)-(2+√-8)

Answer 1

`-11-6√(2)\:i`

Explanation:

Given expression:

`\left(-9-√(-32)\right)-\left(2+√(-8)\right)`

Remove the parentheses:

`\implies -9-√(-32)-2-√(-8)`

Rewrite -32 as 16 · 2 · -1 and rewrite -8 as 4 · 2 · -1 :

`\implies -9-√(16 \cdot 2\cdot -1)-2-√(4 \cdot 2\cdot -1)`

`\textsf{Apply radical rule} \quad √(ab)=√(a)√(b):`

`\implies -9-√(16) √(2) √(-1)-2-√(4)√(2)√(-1)`

Simplify and apply the imaginary number rule √(-1) = i

`\implies -9-4√(2)\:i -2-2√(2)\:i`

Group like terms:

`\implies -9-2-4√(2)\:i -2√(2)\:i`

Combine like terms:

`\implies -11-6√(2)\:i`

Answer 2

• 
  `-11-6i√(2)`

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Simplify the expression:

• 
  `(-9-√(-32) )-(2+√(-8) )=`
• 
  `(-9-√(-1*2*16) )-(2+√(-1*2*4) )=`
• 
  `(-9-4i√(2) )-(2+2i√(2) )=`
• 
  `-9-4i√(2) -2-2i√(2) =`
• 
  `-11-6i√(2)`