Question

1. Find the cube root of the following numbers using the prime factorisation method :
(f). 32768​

Answer 1

Answer:

answer in 32

Step-by-step explanation:

number as it will help in finding the factors of the number easily.

Complete step by step answer:

The question asks us to find the cubic root of 32768. To solve our problem, the first step would be to prime factorize our number which is equal to 32768.

To find the cubic root of our number using the method of prime factorization, we will write the number as a product of its prime factors. The prime factorization of 32768 can be done as follows:

2|32768−−−−−2|16384−−−−−2|8192−−−−−2|4096−−−−−2|2048−−−−−2|1024−−−−−2|512−−−−2|256−−−−2|128−−−−2|64−−−2|32−−−2|16−−−2|8−−2|4−−2|2−−|1−−

Now that we have prime factorized 32768. On substituting 32768 with the product of its prime factors, we get the following equation:

⇒32768=(2×2×2)×(2×2×2)×(2×2×2)×(2×2×2)×(2×2×2)

Now taking cube roots on both side of the equation, we get:

⇒32768−−−−−√3=(2×2×2)×(2×2×2)×(2×2×2)×(2×2×2)×(2×2×2)−−−−−−−−−−−−−−−−−−−−−⎷

Taking out the numbers which repeat three times out of the cubic root, we get our new equation as:

⇒3