Question

Rationalise the denominator
$1 \div \sqrt{5 + \sqrt{2} }$
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Answer 1

Given:

• Rationalise the denominator 1/√5+√2.

Solution:

• Multiplying numerator and denominator by (√5-√2),

⇒ (√5-√2)/(√5+√2)(√5-√2)

⇒ (√5-√2)/(√5)²-(√2)²

• By using algebraic identity, (a+b) (a-b) = a²-b²,

⇒ (√5-√2)/5-2

⇒ (√5-√2)/3

Hence, 1/√5+√2 = (√5-√2)/3.

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