Question

Solve for x. x³ = 216 Enter your answer in the box. x =

Answer 1

$x^3=216\\x=\sqrt[3]{216}=6$

This is a simple example. You (should) know that $6^3=216$.

But you can solve it like this:

$\begin{array}{r|l}216&2\\108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}$

Therefore

$\sqrt[3]{216}=\sqrt[3]{2^3\cdot3^3}=\sqrt[3]{2^3}\cdot\sqrt[3]{3^3}=2\cdot3=6$

Answer 2

Hi student, let me help you out! :)

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We are asked to find the value of x in the equation $\pmb{x^3=216}$.

$\triangle~\fbox{\bf{KEY:}}$

• The goal is to get x all by itself on one side of the equal sign.

Is x by itself? No, it's cubed, or multiplied times itself three times.

So we need to use the opposite operation.

The opposite of cubing is taking the cube root, so we take the cube root of both sides:

$\star~\large\pmb{\sqrt[3]{x^3}=\sqrt[3]{216}}$

On the left, the cube root sign and the cube cancel, because they're opposite, and we're left with x.

On the right, we take the cube root of 216, which gives us:

$\star~\large\pmb{x=6}$

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)