Question

rationalise the denominator of 1/
√3- √5​

Answer 1

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Answer 2

Given

• Rationalize → 1/√3 - √5

Solution

→ 1/√3 - √5

★ Rationalize its denominator

→ 1/√3 - √5 × √3 + √5/√3 + √5

→ √3 + √5/(√3)² - (√5)²

Apply identity :

a² - b² = (a + b)(a - b)

→ √3 + √5/3 - 5

→ √3 + √5/(-2)

→ -(√3 + √5)/2

Extra Information

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