# my question is from chapter square root and cube root how to find the cube root of any number? Please fast

Dear Student

One method of determining whether the number is a perfect cube or not is using the method of prime factorization.

Consider a number 15625 and let us check whether it is a perfect cube or not.

On prime factorizing 5625,we get

5625 = 5 × 5 × 5 × 5 × 5 × 5 = 5 × 5 × 5 × 5 × 5 × 5

Here, all the prime number occurs in combination of 3.

If the prime numbers doesn't occur in combination of 3, then the given number will not be a perfect cube.

Hence, the given number 15625 is a perfect cube of 5 × 5 = 25.

For finding the cube by column method use the following formula:-

(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

Here we take a = tens digit , and b = ones digit ,

For example , we have to find value of 43^{3}

Here a = 4 and b = 3 , and we form column As , and follow these steps :

Step 1 - starting from column I , we take the ones digit , and add the remaining in the column II .

Step 2 - After addition we retain the ones digit and transferred the rest in column III for addition .

Step 3 - After addition we retain the ones digit and transferred the rest in column IV for addition .

Step 4 - After addition we retain all the digits as we don't have any more coulmn .

Step 5 - Now we write all the retained number together to obtain required cube .

Column IV | Column III | Column II | Column I |

a^{3} | 3a^{2}b | 3ab^{2} | b^{3} |

4^{3}= 64 = 64 + 15 = 79 | 3 ( 4 )^{2} ( 3 )= 9 ( 16 ) = 144 = 144 + 11 = 155 | 3 ( 4 ) ( 3 )^{2}= 12 ( 9 ) = 108 = 108 + 2 = 110 | 3^{3}= 27 |

79 | 5 | 0 | 7 |

SO,

**43 ^{3} **

**= 79507 ( Ans )**

The cube root of a number can be evaluated by using the factorization method and approximation method. The method of long division can be used to evaluate the square root of a given number. Long division method is not used to evaluate the cube root of the given number.

Consider the number 97336. Its cube root can be evaluated using the factorization method and approximation method.

**Factorization Method:**

Prime factorization of 97336 = 2 × 2 × 2 × 23 × 23 × 23

Thus, cube root of 97336 is 46.

**Approximation Method:**

Regards

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