Questions & Answers

Question

Answers

Answer
Verified

The prime number is the number which is either divisible by 1 or by itself. (e.g. 2, 3, 5, 7, 11).

Let’s find the cube root of the number using the factorization method first we will factorize the given numbers only by the prime numbers.

\[

2\underline {\left| {10648} \right.} \\

2\underline {\left| {5324} \right.} \\

2\underline {\left| {2662} \right.} \\

11\underline {\left| {1331} \right.} \\

11\underline {\left| {121} \right.} \\

11\underline {\left| {11} \right.} \\

\underline {\left| 1 \right.} \\

\]

Hence we can write \[\left( {10648} \right) = 2 \times 2 \times 2 \times 11 \times 11 \times 11\]

Now make triplet group of the factors of 10648:

\[

\left( {10648} \right) = \left[ {2 \times 2 \times 2} \right] \times \left[ {11 \times 11 \times 11} \right] \\

\sqrt[3]{{\left( {10648} \right)}} = 2 \times 11 = 22 \\

\]

Hence the cube root of 10648 is 22.

Additional Information: To check whether 22 is the cube root of 10648 or not we will find the cube of the number,

\[{\left( {22} \right)^3} = 22 \times 22 \times 22 = 10648\]

Hence we can say 22 is the cube root of 10648.