Question

Evaluate using identity : (5.5)2​

Answer 1

Solution:

To Determine:- The value of 5.5² using identity.

We can calculate the value using 2 ways.

1. Using identity (a + b)² = a² + 2ab + b²

We have:-

= (5.5)²

= (5 + 0.5)²

Using the above mentioned identity, we get:-

= (5)² + 2 × 5 × 0.5 + (0.5)²

= 25 + 5 + 0.25

= 30.25

→ 5.5² = 30.25

2. Using identity (a - b)² = a² - 2ab + b²

We have:-

= (5.5)²

= (6 - 0.5)²

Using the above mentioned identity, we get:-

= (6)² - 2 × 6 × 0.5 + (0.5)²

= 36 - 6 + 0.25

= 30.25

→ 5.5² = 30.25

★ Which is our required answer.

Learn More:

Algebraic Identities.

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab