Estimate cube roots

key notes :

Taking the cube root (∛) is the inverse of cubing. For example, ∛8=2, since 8=2³.

A perfect cube is the result when an integer is multiplied by itself, and then multiplied by itself again. For example, 8 is a perfect cube because 2.2.2=8.

Approximating cube roots

You can approximate cube roots for numbers that are not perfect cubes. Use what you know about perfect cubes to help!

Let’s try it. Approximate ∛80 by finding the two decimals to the hundredths place that ∛80 is between.

The number 80 is not a perfect cube, so find the two perfect cubes that are nearest to 80. The nearest perfect cube that is less than 80 is 64, and the nearest perfect cube that is greater than 60 is 125.

• ∛64=4
• ∛80=?
• ∛125=5

Since ∛64=4 and ∛125=5, then ∛80 must be between 4 and 5. So, pick a value between 4 and 5, and cube it. Cube 4.5.

4.5³=91.125

Since 4.5³ is greater than 80, a cube root of 4.5 is too large. Try a smaller value. Cube 4.4.

4.4³=85.184

Since 4.3³ is greater than 80, a cube root of 4.4 is still too large. Try a smaller value. Cube 4.3.

4.3³=79.507

Since 4.3³ is less than 80, a cube root of 4.3 is too small. Since a cube root of 4.3 is too small and a cube root of 4.4 is too big, ∛80 must be between 4.3 and 4.4. So, pick a value between 4.3 and 4.4, and cube it. Cube 4.32.

4.32³=80.621568

Since 4.32³ is greater than 80, a cube root of 4.32 is too large. Try a smaller value. Cube 4.31.

4.31³=80.062991

Since 4.31³ is greater than 80, a cube root of 4.31 is still too large.

A cube root of 4.3 is too small and a cube root of 4.31 is too big. So, ∛80 must be between 4.30 and 4.31.

Learn with an example

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