Video: Solving Simple Cubic Equations

Solve 𝑥³ = 9.


Video Transcript

Solve 𝑥 cubed is equal to nine.

In order to solve this equation, we need to cube-root both sides. On the left-hand side, we have the cube root of 𝑥 cubed. And on the right-hand side, we have the cube root of nine. As cubing and cube-rooting are inverse operations, the left-hand side just becomes 𝑥. Therefore, 𝑥 is equal to the cube root of nine.

The solution to the equation 𝑥 cubed equals nine is 𝑥 is equal to the cube root of nine. We could work out a decimal answer using our calculator. Typing in the cube root of nine gives us 2.0800838 and so on. Rounding this to two decimal places would give us that the cube root of eight is equal to 2.08 to two decimal places. We could check this on the calculator by typing in 2.08 cubed. This is equal to 8.9989 and so on, which can be rounded up to nine.

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