Question

Find the cube root of 175616 using prime factorisation method.

Answer 1

Primee Factors of 175616 =2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7

Which is the same as = 29 x 73

Prime Factors Tree of 175616

175616 

/     \
2     87808

/       \
2      43904

/       \
2      21952

/       \
2      10976

/       \
2      5488

/       \
2      2744

/       \
2      1372

/       \
2      686

/       \
2      343

/       \
7      49

/       \
7      7

/       \
7      1

Answer 2

Answer:

56

Step-by-step explanation:

Given : Number = 175616

To Find : Cube root

Solution:

Prime factorization

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

$175616= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\times 2 \times 2 \times 7 \times 7 \times 7$

$175616=2^3 \times 2^3 \times 2^3 \times 7^3$

$175616=2^3 \times 2^3 \times 2^3 \times 7^3$

$\sqrt[3]{175616}=\sqrt[3]{2^3 \times 2^3 \times 2^3 \times 7^3}$

$\sqrt[3]{175616}=2\times 2 \times 2 \times 7$

$\sqrt[3]{175616}=56$

Hence the cube root of 175616 is 56