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Find the cube root of the following number by prime factorization method: 175616.

Find the cube root of the following number by prime factorization method: 175616.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
20 days ago
Hint: Use the prime factorization method to find the prime factors of 175616. Then form triplets of the same prime numbers from the prime factors of 175616 and then take the cube root and simplify. Complete step-by-step answer: Cube root of a number is the number which when multiplied with itself three times gives the first number. The cube root of 175616 can be found using the prime factorization method to obtain the prime factors of 175616 and then find the cube root of them. In this method, the number 175616 is divided by the first prime number 2 and the quotient obtained. The quotient is again divided by 2 and so on until we get a remainder. Then, we divide the resultant with the next prime number 3 and so on until we get the remainder. This is continued with other prime numbers until we get the final number as 1. Let's factorize the number 175616 using prime factorization as below: Hence, we can represent 175616 as the product of primes as below: 175616=2×2×2×2×2×2×2×2×2×7×7×7 Grouping the factors to form the triplet, we have: 175616=2×2×2−−−−−−−−×2×2×2−−−−−−−−×2×2×2−−−−−−−−×7×7×7−−−−−−−− Taking the cube root, we have: 175616−−−−−−√3=2×2×2×7 Simplifying, we have: 175616−−−−−−√3=56 Hence, the cube root of 175616 is 56. Note: You can multiply the answer three times to check if you get back the number 175616. You can not use any other method to find the cube root, since it is specified that you need to solve using the prime factorization method.

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