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Q.

Find the cube-root of 13824 by the method of prime factorization.

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a

24

b

18

c

12

d

36

answer is A.

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Detailed Solution

Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than 1 and which are not the product of any two smaller natural numbers.
To find the prime factorisation, start dividing the given number 13824 by the first prime number, 2 Continue division until it is not divisible by 2 . Gradually start dividing by 3, 5, 7, 11, 13,....
⇒13824 = 2×2×2×2×2×2×2×2×2×3×3×3
When the same number is multiplied thrice, it can be written as a cube of the number.

\Rightarrow 13824 = 2^{3} \times 2^{3} \times 2^{3} \times 3^{3}

Take cube root on both the sides of the equation –

\Rightarrow \sqrt[3]{13824} = \sqrt[3]{2^{3} \times 2^{3} \times 2^{3} \times 3^{3}}

Cube and cube-root cancel each other on the right side of the equation.

\Rightarrow \sqrt[3]{13824} = 2 \times 2 \times 2 \times 3

Simplification-

\sqrt[3]{13824} = 24

So, the correct answer is “Option 1”.

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