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}

Answer: Steps are given below,

  • 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}.

Answer: Steps are given below,

  •  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.

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