Answer:
[tex]\boxed{ \red{ \frac{10 + 2 \sqrt{3} }{11}} }[/tex]
Step-by-step explanation:
Given equations is
[tex] \frac{4}{5 - \sqrt{3} } [/tex]
Rationalise
[tex] \frac{4}{5 - \sqrt{3} } \times \frac{5 + \sqrt{3} }{5 + \sqrt{3} } [/tex]
Solve
[tex] \frac{20 + 4 \sqrt{3} }{ ( {5}^{2}) - ( { \sqrt{3} }^{2} ) } [/tex]
As we know
[tex]\therefore \: \: \: \: \: \: (a - b)(a + b) = {a}^{2} - {b}^{2} [/tex]
[tex] \frac{20 + 4 \sqrt{3} }{25 - 3} [/tex]
[tex] \frac{20 + 4 \sqrt{3} }{22} [/tex]
Split denominator
[tex] \frac{20}{22} + \frac{4 \sqrt{3} }{22} [/tex]
[tex]\boxed{ = \frac{10 + 2 \sqrt{3} }{11}} [/tex]
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Verified answer
Answer:
[tex]\boxed{ \red{ \frac{10 + 2 \sqrt{3} }{11}} }[/tex]
Step-by-step explanation:
Given equations is
[tex] \frac{4}{5 - \sqrt{3} } [/tex]
Rationalise
[tex] \frac{4}{5 - \sqrt{3} } \times \frac{5 + \sqrt{3} }{5 + \sqrt{3} } [/tex]
Solve
[tex] \frac{20 + 4 \sqrt{3} }{ ( {5}^{2}) - ( { \sqrt{3} }^{2} ) } [/tex]
As we know
[tex]\therefore \: \: \: \: \: \: (a - b)(a + b) = {a}^{2} - {b}^{2} [/tex]
[tex] \frac{20 + 4 \sqrt{3} }{25 - 3} [/tex]
[tex] \frac{20 + 4 \sqrt{3} }{22} [/tex]
Split denominator
[tex] \frac{20}{22} + \frac{4 \sqrt{3} }{22} [/tex]
Solve
[tex]\boxed{ = \frac{10 + 2 \sqrt{3} }{11}} [/tex]