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Find the cube root of each of the following numbers by prime factorisation method. (ix) 175616 (x) 91125

 Find the cube root of each of the following numbers by prime factorisation method.

 

(ix) 175616

(x) 91125

Grade:12th pass

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
one year ago
Dear Student

(ix) 175616

Solution:

175616 = 2×2×2×2×2×2×2×2×2×7×7×7

By grouping the factors in triplets of equal factors,

175616 = (2×2×2)×(2×2×2)×(2×2×2)×(7×7×7)

Here, 175616 can be grouped into triplets of equal factors,

∴ 175616 = (2×2×2×7) = 56

Hence, 56 is cube root of 175616.

(x) 91125

Solution:

91125 = 3×3×3×3×3×3×3×5×5×5

By grouping the factors in triplets of equal factors, 91125 = (3×3×3)×(3×3×3)×(5×5×5)

Here, 91125 can be grouped into triplets of equal factors,

∴ 91125 = (3×3×5) = 45

Hence, 45 is cube root of 91125.​



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