Question

find the cube root of 4.096 step by step on page​

Answer 1

Answer:

The cube root of a number is denoted by ∛  

The cube root of a number x is that number whose cube gives x. We denote the cube root of x by ∛x  

Thus, 3√64 = cube root of 64 = 3∛4 × 4 × 4 = ∛4³ = 4

For example:  

(i) Since (2 × 2 × 2) = 8, we have ∛8 = 2  

(ii) Since (5 × 5 × 5) = 125, we have ∛125 = 5  

Step-by-step explanation:By prime factorization, we have  

216 = 2 × 2 × 2 × 3 × 3 × 3  

= (2 × 2 × 2) × (3 × 3 × 3)  

Therefore, ∛216 = (2 × 3) = 6  

2. Evaluate the cube root: ∛343

Solution:  

By prime factorization, we have  

343 = 7 × 7 × 7  

= (7 × 7 × 7).  

Therefore, ∛343 = 7

3. Evaluate the cube root: ∛2744

Solution:  

By prime factorization, we have

2744 = 2 × 2 × 2 × 7 × 7 × 7

= (2 × 2 × 2) × (7 × 7 × 7).  

Therefore, ∛2744 = (2 × 7) = 14