Question

$\sqrt{\frac{p}{2}-2 } = \sqrt{p-8}$

Answer 1

$\boldsymbol{\sqrt{\dfrac{p}{2}-2}=\sqrt{p-8}}$

Cancel the square root on both sides.

• $\boldsymbol{\sf{\dfrac{p}{-2}-2=\sqrt{p-8} }}$

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

$\boldsymbol{\sqrt{\dfrac{p}{2}-2}=\sqrt{p-8} \ \ \to \ \ \ Exercise \ normal.}$

Let p=12.

• $\boldsymbol{\sqrt{\dfrac{12}{2}-2}=\sqrt{12-8}}$

Simplify 12/6 to 6.

• $\boldsymbol{\sqrt{6-4}=\sqrt{12-8} }$

Simplify 6-2 to 4.

• $\boldsymbol{\sqrt{4}=\sqrt{12-8} }$

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

• $\boldsymbol{2=\sqrt{12-8} }$

Simplify 12-8 to 4.

• $\boldsymbol{2=\sqrt{4} }$

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

• $\boldsymbol{2=2}$

Checked ✅

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

Answer 2

2=2^
Explained above