Question

`\sqrt{(p)/(2)-2 } = √(p-8)`

Answer 1

2=2^
Explained above

Answer 2

`\boldsymbol{\sqrt{(p)/(2)-2}=√(p-8)}`

Cancel the square root on both sides.

• 
  `\boldsymbol{\sf{(p)/(-2)-2=√(p-8) }}`

Multiply both sides by 2.

• 
  `\boldsymbol{\sf{p-4=2p-16 }}`

Subtract p from both sides.

• 
  `\boldsymbol{\sf{-4=2p-16-p }}`

Simplify

• 
  `\boldsymbol{\sf{-4=p-16 }}`

Add 16 to both sides.

• 
  `\boldsymbol{\sf{-4+16=p }}`

Simplify

• 
  `\boldsymbol{\sf{12=p}}`

Swap sides.

• 
  `\boldsymbol{\sf{p=12 \ \ \to \ \ \ Answer}}`

↓

Verification

`\boldsymbol{\sqrt{(p)/(2)-2}=√(p-8) \ \ \to \ \ \ Exercise \ normal.}`

Let p=12.

• 
  `\boldsymbol{\sqrt{(12)/(2)-2}=√(12-8)}`

Simplify 12/6 to 6.

• 
  `\boldsymbol{√(6-4)=√(12-8) }`

Simplify 6-2 to 4.

• 
  `\boldsymbol{√(4)=√(12-8) }`

Since 2×2=4, the square root of 4 is 2.

• 
  `\boldsymbol{2=√(12-8) }`

Simplify 12-8 to 4.

• 
  `\boldsymbol{2=√(4) }`

Since 2×2=4, the square root of 4 is 2.

• 
  `\boldsymbol{2=2}`

Checked ✅

`\huge \red{\boxed{\green{\boxed{\boldsymbol{\sf{\purple{Pisces04}}}}}}}`