Question

Rationalize the denominator
$\frac{1}{\sqrt{5 - \sqrt{3} } }$
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Answer 1

Correct Question :

Rationalize the denominator :

$\longmapsto\tt{\dfrac{1}{\sqrt{5}-\sqrt{3}}}$

Given :

• 1 /√5 - √3 .

To Find :

• Rationalize the denominator .

Solution :

$\longmapsto\tt\bf{\dfrac{1}{\sqrt{5}-\sqrt{3}}}$

$\longmapsto\tt{\dfrac{1}{\sqrt{5}-\sqrt{3}}\times\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}}$

Using Identity :

• (x - y) (x + y) = x² - y²

$\longmapsto\tt{\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{(5)}^{2}-\sqrt{(3)}^{2}}}$

$\longmapsto\tt{\dfrac{\sqrt{5}+\sqrt{3}}{5-3}}$

$\longmapsto\tt\bf{\dfrac{\sqrt{5}+\sqrt{3}}{2}}$

So , The Final Answer is √5 + √3 / 2 ..

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Some More Identities :

• (x + y)² = x² + 2xy + y²
• (x - y)² = x² - 2xy + y²
• x² - y² = (x + y) (x - y)
• (x + a) (x + b) = x² + (a + b)x + ab
• (x + y + z) = x² + y² + z² + 2xy + 2yz +2zx
• (x + y)³ = x³ + y³ + 3xy (x+y)
• (x - y)³ = x³ - y³ - 3xy (x-y)

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