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10 grade maths

Find the cube root of 64 by prime factorization method.

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9 Months agoGrade
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1 Answer

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ApprovedApproved Tutor Answer9 Months ago

To find the cube root of 64 using the prime factorization method, we first need to break down 64 into its prime factors.

Step 1: Prime Factorization of 64

We can divide 64 by the smallest prime number, which is 2:

  • 64 ÷ 2 = 32
  • 32 ÷ 2 = 16
  • 16 ÷ 2 = 8
  • 8 ÷ 2 = 4
  • 4 ÷ 2 = 2
  • 2 ÷ 2 = 1

So, the prime factorization of 64 is:

64 = 2 × 2 × 2 × 2 × 2 × 2 = 26

Step 2: Finding the Cube Root

The cube root of a number is found by taking one-third of the exponent in its prime factorization. Here, we have:

26

To find the cube root:

  • Divide the exponent by 3: 6 ÷ 3 = 2

Final Result

Thus, the cube root of 64 is:

22 = 4

In conclusion, the cube root of 64 is 4.

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