Question

Cube root of -17576 ?

• A. -26
• B. 26
• C. -13
• D. -169

Answer 1

The correct option is A -26

Let's factorize 17576 first.
$\Rightarrow 17576=2\times \left(8788\right)$
$=2\times 2\times \left(4394\right)$
$=2\times 2\times 2\times \left(2197\right)$
$=2\times 2\times 2\times 13\times \left(169\right)$
$=2\times 2\times 2\times 13\times 13\times 13$
$=(2\times 13)\times (2\times 13)\times (2\times 13)$
$=26\times 26\times 26$

$\Rightarrow -17576=(-26)\times (-26)\times (-26)$
$\Rightarrow -\sqrt[3]{317576}=-26$