Question

rationalise the denominator of 1/5+2√3​

Answer 1

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Answer 2

Given :-

• 1/5 + 2√3

To find :-

• Rationalize the denominator

Solution :-

→ 1/5 + 2√3

• Rationalize its denominator

→ 1/5 + 2√3 × 5 - 2√3/5 - 2√3

• Apply identity
• a² - b² = (a + b)(a - b)

→ 5 - 2√3/(5)² - (2√3)²

→ 5 - 2√3/25 - 12

→ 5 - 2√3/13

Hence,

• 5-2√3/13 is the value after rationalising 1/5 + 2√3

Some more identities

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ - b³ - 3ab(a - b)

• a³ - b³ = (a - b)(a² + ab + b²)

• a³ + b³ = (a + b)(a² - ab + b²)