Question

Estimation method is preferably used to find the cube root of _________ .

• A. any number
• B. non-perfect cubes
• C. perfect cubes
• D. non-perfect squares

Answer 1

The correct option is C perfect cubes

Estimation method can be used to find the cube roots of perfect cubes.
Ex:
17576 is a perfect cube number.
Grouping it in threes from right gives $\underset{–}{17}\underset{–}{576}$. Now the unit digit is 6, so the cube root should also have its unit digit as 6 and $2^3<17<3^3$.
Hence, cube root of 17576 is 36.

But if we take any non-perfect number like 7110.
By estimation method we get, $\sqrt[3]{37110}$ as 10. But we know that ${10}^3=1000\ne 7110$.
So, estimation method is only applicable to find cube roots of perfect cubes.