Question

find the cube root of the following numbers by prime factorisation method .( a) -216 (b) -1331 (c) 3.375 (d) 729/1000​

Answer 1

Answer:

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Step-by-step explanation:

(a) -(cuberoot216)

   Prime factorisation of 216 = 2*2*2*3*3*3

   So, cube root is 2*3 = 6

   Therefore the answer is -6.

(b) -(cuberoot1331)

    Prime factorisation of 1331 = 11*11*11

    So, Cube root is 11

    Therefore the answer is -11.

(c) (cuberoot3.375)

    We can re-write 3.375 as 3375/1000, reduced to 31/8

    Prime factorisation of 31 is 1*31 and 8 is 2*2*2

    So, Cube root is (cuberoot31)/2

    Therefore the answer is cuberoot31/ 2.

(d) (cuberoot729/1000)

    Prime factorisation of 729 = 3*3*3*3*3*3 and of 1000 = 10*10*10

    So, Cube root is 9 and 10.

    Therefore the answer is 9/10.