Question

State the number of digits in the cube root of the following cubes
(a) 9261

Answer 1

Hint: We know that a cube root of a number is like asking what is the number which when multiplied by itself three times yields the number 9261. To solve the above question we use factorization method and then we make triplets of same factors and now by reducing triplets to a single factor, we multiply the end factors to find the cube root of whose number of digits is the answer.

Complete step-by-step answer:
To find the cube root of a number, we would like to search a number that when multiplied by itself thrice gives us the original number.
For example –
 If we want to find the cube root of 8, we have to find the number that when multiplied by itself thrice gives you 8. The cube root of 8, written as \[\sqrt[3]{8}\] , is 2, because 2 × 2 × 2 = 8. Notice that the symbol for cube root is the radical sign with a small three written above and to the left \[\sqrt[3]{{}}\]. Other roots are defined similarly and identified by the index given. (In square root, an index of two is understood and usually not written.)

Using the above reasoning we find thr cube root of above number i.e. 9261
We factorize the above number to its prime factors
\[9261=3\times 3\times 3\times 7\times 7\times 7\]
We form triplets of similar factors,
\[9261=(3\times 3\times 3)\times (7\times 7\times 7)\]
To find cube root we need to reduce the above triplets to a single number
\[\sqrt[3]{9261}=(3)\times (7)\]
\[\sqrt[3]{9261}=21\]
Since the answer we get is 21 so the required answer is 2.

Note: The student must be familiar with the concept of cube root and the use of factoring methods used to find the cube root by prime factorization. The common mistake include wrong factorization, inability to count number of triplets, writing the factor instead of finding the number of digits in that number.