Question

√5 - √3 ÷
√5 +√3

please give answer step by step​

Answer 1

Answer:

0.126

Step-by-step explanation:

2.23-1.73/2.23+1.73

=

0.5/3.96

=

= 0.126

Answer 2

$\huge \dag \: \: \: \bf \dfrac{ \sqrt{5} - \sqrt{3} } { \sqrt{5} + \sqrt{3} } \\ \\ \to \tt \dfrac{ \sqrt{5} - \sqrt{3} } { \sqrt{5} + \sqrt{3} } \times \dfrac{ \sqrt{5} - \sqrt{3} } { \sqrt{5} - \sqrt{3} } \\ \\ \to \tt \dfrac{(\sqrt{5} - \sqrt{3})(\sqrt{5} - \sqrt{3})}{(\sqrt{5} + \sqrt{3})(\sqrt{5} - \sqrt{3})}$

• (a - b)(a - b) = (a - b)² = a² + b² - 2ab
• (a + b)(a - b) = a² - b²

Using above mentioned identities, we get,

$\to \tt \dfrac{ {( \sqrt{5} - \sqrt{3} )}^{2} }{ {( \sqrt{5} )}^{2} - {( \sqrt{3} )}^{2} } \\ \\ \to \tt \dfrac{ {( \sqrt{5} )}^{2} + {( \sqrt{3} )}^{2} - 2( \sqrt{5} )( \sqrt{3} ) }{5 - 3} \\ \\ \to \tt \dfrac{5 + 3 - 2 \sqrt{15} }{2} \\ \\ \to \tt \dfrac{8 - 2 \sqrt{15} }{2} = \dfrac{\cancel2(4 - \sqrt{15} )}{ \cancel2} \\ \\ \implies \red{\sf4 - \sqrt{15} }$

Hence,

• 4 - √15 is the rationalised form of (√5 - √3)/(√5 +√3)