Answer:
56
Step-by-step explanation:
Cube root of 175616 by prime factorization method is 56
Solution:
To find cube root of 175616 by prime factorization method
A number that must be multiplied by itself three times to equal a given number is called cube root
Prime factorization method:
Prime factorization is a number written as the product of all its prime factors.
In order of finding cube root by prime factorization we use the following steps:
Step I : Obtain the given number
Step II : Resolve it into prime factors.
Step III : Group the factors in 3 in such a way that each number of the group is same
Step IV : Take one factor from each group
Step V : Find the product of the factors obtained in step IV. This product is the required cube root
Prime factorization of 175616:
\text{ prime factors of 175616 } = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7 prime factors of 175616 =2×2×2×2×2×2×2×2×2×7×7×7
Thus we get,
\sqrt[3]{175616} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7}
3
175616
=
3
2×2×2×2×2×2×2×2×2×7×7×7
Make the groups of 3 of equal numbers
\sqrt[3]{175616} = \sqrt[3]{2 \times 2 \times 2} \times \sqrt[3]{2 \times 2 \times 2 \times } \times \sqrt[3]{2 \times 2 \times 2} \times \sqrt[3]{7 \times 7 \times 7}
3
175616
=
3
2×2×2
×
3
2×2×2×
×
3
2×2×2
×
3
7×7×7
So there are 4 equal groups. So from that group take one factor out
\sqrt[3]{175616} = 2 \times 2 \times 2 \times 7 = 56
3
175616
=2×2×2×7=56
Thus Cube root of 175616 by prime factorization method is 56
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, the LHS reduces to 0, so 
is a factor of the cubic. You can find the remaining two solutions easily with the quadratic formula.