Question

Find the cube root of 175616 by prime factorization method​

Answer 1

Solution:

First find factors of 175616

2 175616

2 87808

2 43904

2 21952

2 10976

2 5488

2 2744

2 1372

2 686

7 343

7 49

7 7

 1

175616=2×2×2×2×2×2×2×2×2×7×7×7

175616=2^9⋅7^3

Taking cuberoot

∴3√175616

=3√2^9⋅7^3

=23×7

=56