Question

Find cube root by prime factorization of 1728
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Answer 1

Answer:

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Step-by-step explanation:

3√1728=3√23×23×33=2×2×3=12.

• 3√1728=3√23×23×33=2×2×3=12.The cube root gets neutralized by the cube of 12.
• 3√1728=3√23×23×33=2×2×3=12.The cube root gets neutralized by the cube of 12.Hence, the cube root of 1728 is 12.
• 3√1728=3√23×23×33=2×2×3=12.The cube root gets neutralized by the cube of 12.Hence, the cube root of 1728 is 12.Find the cube root of 175616 by estimation method.
• 3√1728=3√23×23×33=2×2×3=12.The cube root gets neutralized by the cube of 12.Hence, the cube root of 1728 is 12.Find the cube root of 175616 by estimation method.Solution:

The first part of 175616 is 616 and the second part is 175.

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Answer 2

Step 1: Find the prime factors of 1728

1728 = 2x2x2x2x2x2x3x3x3

Step 2: Group the factors in a pair of three and write in the form of cubes.

1728 = (2x2x2)x(2x2x2)x(3x3x3)

1728 = 2³x2³x3³

Step 3: Apply cube root both the sides and take out the terms in cubes out of the cube root.

3√1728 = 3√(2³x2³x3³) = 2 x 2 x 3 = 12

Hence, 3√1728 =12