Cube roots of perfect cubes

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Basic Cube Values

1st of all we need to remember the cubes of number ranging from 1 to 10. Below the cubes of this number is given in table form:-

 Number Cube 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000

Last Digits of Cube Roots

Another table we need to remember for evaluating cube roots is given below:-

 Last digit of the cube Last digit of the cube roots 1 1 2 8 3 7 4 4 5 5 6 6 7 3 8 2 9 9 0 0

Now take some example:-

Examples

Example 1: Find $\sqrt[3]{941192}$

Answer: – Detailed step is given below

•   1st of all write the number as two pair of three digits each, 941 192.
•   Since cube ends with 2 so last digit of the cube root is 8. (As given in the above table).
•  Now the left pair of the number is 941. So it lies between 729($\sqrt[3]9$) and 1000(  $\sqrt[3]{10}$).
• Now out of 9and 10 smaller number is 9, so we take 9 as the left part in the answer and put it left to the 8. So final answer is 98.

Example 2: Find   $\sqrt[3]{1367631}$

• Here we have to divide the number as 1367 631 (Remember, 2 nd part always consist of last three digit number).
• Now last digit of cube is 1 so last digit of the cube root is 1. We get the extreme right part of the cube root.
• Now the left part 1367 lies between 1331( $\sqrt[3]{11}$) and 1728($\sqrt[3]{12}$).
• So smaller number between 11 and 12 is 11. So the left part of $\sqrt[3]{11}$. The answer is 111.

Example 3: Find $\sqrt[3]{79507}$.

•  Here we have to divide the number as 79 507
• Now last digit of the cube is 7,so last digit of the cube root 3.We get the right part of the answer as 3.
• Now the left part lies between 64($\sqrt[3]{4}$) and 125($\sqrt[3]{5}$).
• So the smaller number between 4 and 5 is 4.
• So the answer is 43.