Estimating the Cube Root of a Number

If we know that the given number is a cube number, then to find its cube root, we can use the following method.

Let us find the cube root of 15,625 through estimation.

Step 1: Start making groups of three digits starting from the unit place i.e., 15,625 15 │ 625 first│ second group│ group

Step 2: First group i.e. 625 will give us the units digit of the cube root. As 625 ends with , its cube root also ends with . So, the units place of the cube root will be .

Step 3: Now, take first group i.e. 15 We know that < 15 < . As the smallest number is , it becomes the tens place of the required cube root.

∴ ∛15,625 =

To verify: 25³ = × × =

This method helps us find cube roots by:

(1) Grouping digits in threes from the right

(2) Finding the units digit based on the last group

(3) Finding the tens digit by comparing cubes of numbers with the first group

Chapter 6: Square Roots and Cube Roots

Glossary

Estimating the Cube Root of a Number

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Chapter 6: Square Roots and Cube Roots

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Glossary

Estimating the Cube Root of a Number