Question

Using suitable identity, find the value of (1.1)³.

Answer 1

Given: Find the value of (1.1)³ using a suitable algebraic identity.

Step-wise calculation:

1. Recognize that (1.1 = 1 + 0.1), so we can use the binomial cube identity:

(1 + x)³ = 1³ + 3 × 1² × x + 3 × 1 × x² + x³

(1 + x)³ = 1 + 3x + 3x² + x³

where (x = 0.1).

2. Substitute (x = 0.1) into the identity:

(1.1)³ = 1 + 3(0.1) + 3(0.1)² + (0.1)³

3. Calculate each term:

3(0.1) = 0.3

3(0.1)² = 3 × 0.01

3(0.1)² = 0.03

(0.1)³ = 0.001

4. Add these values together:

1 + 0.3 + 0.03 + 0.001 = 1.331

Thus, the value of (1.1)³ using the binomial identity is 1.331.