If z is negative, then [4](4z-5)^4 + (3-2z)^2 + -z |z| = ?

If z is negative, then [4](4z-5)^4 + (3-2z)^2… | GMAT Sprint

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PS · Problem Solving

705-805

Roots

If z is negative, then $\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|} = ?$

Answer Choices

Correct answer marked below

3z-2

z-2

-8

8-7z

Correct

4z-8

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Explanation

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Official Explanation

Official

Concept Tested:

\sqrt{x^2} = |x|

|x| = x

, when

x \geq 0

|x| = -x

, when

x < 0

\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|}

As z is negative, |z| = -z

\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z (-z)}

\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{z^2}

…

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What this question tests

What it tests

Your handling of square and higher roots, including simplifying radicals.

Common trap

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

If z is negative, then (4z−5)44+(3−2z)2+−z∣z∣=?\sqrt[4]{(4z-5)^4} + \sqrt{(3-2z)^2} + \sqrt{-z |z|} = ?4(4z−5)4​+(3−2z)2​+−z∣z∣​=?