Question

find the cube root of 166.375 by factorization method

Answer 1

Given:

The number 166.375

To find:

Its cube root by factorization method

Step-by-step explanation:

Now, 166.375 = 166375/1000

Here we prime factorize both the numerator and the denominator separately.

5 | 166375

5 | 33275

5 | 6655

11 | 1331

11 | 121

11

So, 166375 = 5 × 5 × 5 × 11 × 11 × 11

2 | 1000

2 | 500

2 | 250

5 | 125

5 | 25

5

So, 1000 = 2 × 2 × 2 × 5 × 5 × 5

Now, 166375/1000

= (5 × 5 × 5 × 11 × 11 × 11) / (2 × 2 × 2 × 5 × 5 × 5)

= (11 × 11 × 11) / (2 × 2 × 2)

⇒ 3√(166375/1000) = 3√[(11 × 11 × 11) / (2 × 2 × 2)]

⇒ 3√(166375/1000) = 11/2

⇒ 3√(166375/1000) = 5.5

Answer: Cube root of 166.375 is 5.5