Question

Solve this 5/(√3-√5)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

ANSWER:

${ \tt{ \to \dfrac{5}{ \sqrt{3} - \sqrt{5} } }}$

Rationalizing the denominator

${ \tt{ \implies \dfrac{5( \sqrt{3} + \sqrt{5} )}{( \sqrt{3} - \sqrt{5})( \sqrt{3} + \sqrt{5}) } }}$

Using

(a + b)(a - b) = a² - b²

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

Hence,

$\frac{5}{ \sqrt{3} - \sqrt{5} } \to \frac{ - 5( \sqrt{3} + \sqrt{5} ) }{2} = - 9.9023$

CONCEPTS USED:

→ Algebraic identities

→ Surds

MORE INFORMATION:

$\small{ \sf{ \to \sqrt[m]{ \sqrt[n]{a} } = \sqrt[mn]{a} }}$

$\small{ \sf{ \to {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab }}$

$\small{ \sf{ \to {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab }}$