Question

find the cube root of the following numbers using prime factorization 17576​

Answer 1

Answer:

Hint: To find the cube root of the number we factorize the given number until we get a number which is raised to the power of 3. We express the number 17576 as a product of prime numbers. = 26 × 26 × 26. This shows that −17567 = (−26) × (−26) × (−26).

Answer 2

Prime factorization:

2 | 17576

2 | 8788

2 | 4394

13| 2197

13| 169

13| 13

| 1

So, 17576=2×2×2×13×13×13

$17576=2^3 \times 13^3$

$\sqrt[3]{17576}=\sqrt[3]{2^3 \times 13^3}$

$\sqrt[3]{17576}=3 \times 13$

$\sqrt[3]{17576}=39$

So, the cube root by prime factorization 17576 is 39