Question

10) Solve a = -64 A. a = -32 B. a=-8 C. a = -4 D. a = -21 Continue: Turn to the next pa Pad PST

Answer 1

This is a radical equation.

$a^3=-64$

This basically tells us what number multiplied by itself 3 times gives an answer of -64?

To algebraically solve it, we need to isolate a. To do this, we take the cube root of both sides. The cube root and cube gets cancelled and we are left with a. Shown below:

$\begin{gathered} a^3=-64 \\ \sqrt[3]{a^3}=\sqrt[3]{-64} \\ a=\sqrt[3]{-64} \end{gathered}$

So, what is the cube root of -64?

It is "-4" because:

$-4\times-4\times-4=-64$

Thus,

$\begin{gathered} a=\sqrt[3]{-64} \\ a=-4 \end{gathered}$

The correct answer is C