# [Important examples]Finding cube root using factorization method

In this post, we’re going to find cube root using the factorization method. But, you haven’t learned the basic procedure for cube root using the factorization method, check this article. In this post, I have covered every step with images and at the end you will get examples as well as practice problems with answer.

Q.1 Find the cube root of 512 using the prime factorization method.

Solution:

Using factorization method ,find the prime factor of 512 512= 2×2×2×2×2×2×2×2×2

Make triplets of prime factors

512= 2×2×2× 2×2×2× 2×2×2

3√512=32×2×2× 2×2×2× 2×2×2

3√512=2×2×2

3√512=8

Hence ,cube root of 512 is 8

Q.2 Find the cube root of 15625 using the prime factorization method.

Solution:

Using factorization method ,find the prime factors of 15625 15625= 5 × 5 ×5 ×5 ×5 ×5

Make triplets of prime factors

3√15625=3√5 × 5 ×5 ×5 ×5 ×5

3√15625=5×5×5

3√15625=125

Hence , cube root of 15625 is 125 .

Q.3 Find the cube root of 27000 using the prime factorization method.

Solution:

Using factorization method ,find prime factors of 27000 27000= 2×2×2×3×3×3×5×5×5

3√27000=3√2×2×2×3×3×3×5×5×5

3√27000=2×3×5

3√27000=30

Hence ,cube root of 27000 is 30

Q.4 Find the cube root of 110592 using the prime factorization method.

Solution:

Using factorization method ,find prime factor of 110592 110592= 2×2×2×2×2×2×2×2×2×2×2×2×3×3×3

3√110592=3√2×2×2×2×2×2×2×2×2×2×2×2×3×3×3

3√110592= 2×2×2×2×3

3√110592=48

Hence , cube root of 110592 is 48 .

Q.5 Find the cube root of 175616 using the prime factorization method.

Solution:

Using factorization method ,find the prime factor of 175616 175616= 2×2×2×2×2×2×2×2×2×7×7×7

3√175616=3√2×2×2×2×2×2×2×2×2×7×7×7

3√175616=2×2×2×7

3√175616=56

Hence ,cube root of 175616 is 56

Q.6 Find the cube root of 91125 using the prime factorization method .

Solution:

Using factorization method ,find the prime factor of 91125 91125= 5×5×5×3×3×3×3×3×3

3√91125=3√5×5×5×3×3×3×3×3×3

3√91125=5×3×3

3√91125=45

Hence ,cube root of 91125 is 45 .

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