Solve x^3 = -27/125 Step by Step | Solve x² = 49 and x³ = 27

Step by step

Question: solve x³ = −27/125.

x³ = −27125

x³ means x times x times x.

We want just x.

x³ = x × x × x

The cube root asks: which number, times itself three times, makes this?

∛27 = ? → ? × ? × ? = 27

The cubes: 1 times 1 times 1 is 1.

2 times 2 times 2 is 8.

3 times 3 times 3 is 27.

4 times 4 times 4 is 64.

5 times 5 times 5 is 125.

1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125

x is the cube root of −27/125.

x = ³√27125

A negative number, times itself three times, stays negative: minus times minus is plus, times minus again is minus.

(−3)³ = − × − × − = −

We take the cube root of the top and of the bottom.

3 cubed is 27.

5 cubed is 125.

x = ³√27³√125

So x = −3/5.

x = −35

Careful!

With squares, a negative has no root.

With cubes it does: the answer is negative.

Careful: a negative number has a cube root

Let's check: −3/5 times −3/5 times −3/5 is −27/125.

−35 × −35 × −35 = −27125

The same as the right side.

So the answer is right!

Let's look back.

First: cube root of both sides.

Last: check.

Answer

Careful: a negative number has a cube root