Question

Find the cube root of 45 × 180 × 90​

Answer 1

Given: Three numbers 45, 180, and 90

To find: Cube root of 45 x 180 x 90

Solution:

To find the cube root of any number:

• Write the prime factorization of the given numbers
• Pair the same numbers in the group of 3
• Take out one number from each group and then multiply them.

Prime factorization of 45 = 3 x 3 x 5, 180 = 2 x 2 x 3 x 3 x 5, 90 = 2 x 3 x 3 x 5

Therefore, prime factorization of

45 x 180 x 90 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5

Making the pairs of three: 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5

Now, the cube root of the given number = 2 x 3 x 3 x 5 = 90

Hence, Cube root of 45 x 180 x 90 = 90.