Question

Rationalise the denominator.
1/4+✓2+✓5​

Answer 1

Answer:

hope this ans is help ful for you

Answer 2

Answer:

Given:     1/(4+✓2+✓5​)

Now rationalising the denominator,

⇒ [1/(4+✓2+✓5​)] × 4 - ✓2+✓5​/ 4 - ✓2+✓5

⇒ 4 - ✓2+✓5 / (4+✓2+✓5​)(4 - ✓2+✓5)

⇒ 4 - ✓2+✓5 / (4)² - (✓2+✓5)

⇒ 4 - ✓2+✓5 / 16 - (2 + 5 - 2√10)

⇒ 4 - ✓2+✓5 / 16 - 7 + 2√10

⇒ 4 - ✓2+✓5 / 9 + 2√10

now again rationalising the denominator,

⇒ (4 - ✓2+✓5 /  9 + 2√10 ) × (9 - 2√10 / 9 - 2√10)

⇒ (4 - ✓2+✓5)(9 - 2√10 ) / (9)² - (2√10)²

⇒ {9 (4 - ✓2+✓5) - 2√10 (4 - ✓2+✓5)} / 81 - 40

⇒{ 36 - 9(✓2+✓5) - 8√10 + 2√10(✓2+✓5) } / 41

∴ So the correct answer is

          = { 36 - 9(✓2+✓5) - 8√10 + 2√10(✓2+✓5) } / 41

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