Question

Answer this

On rationalizing the denominator of
$1 \div \sqrt{7} - \sqrt{6}$
we get

​

Answer 1

Step-by-step explanation:

1/√7-√6

1/√7(√7÷√7)-√6

(√7/7)-√6

(√7-7√6)/7

Answer 2

Given

1/√7 - √6

Rationalize its denominator

Solution

→ 1/√7 - √6

→ 1/√7 - √6 × √7 + √6/√7 + √6

★ Applying identity :

a² - b² = (a + b)(a - b)

→ √7 + √6/(√7)² - (√6)²

→ √7 + √6/7 - 6

→ √7 + √6/1

→ √7 + √6

Some identities

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