Answer:
8 - 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given: [tex]\frac{26}{4 + \sqrt{3} }[/tex]
To express the given question in the form a + b[tex]\sqrt{3}[/tex], we first have to rationalize the denominator of the expression.
Rationalizing the denominator, we have;
[tex]\frac{26}{4 + \sqrt{3} }[/tex] * [tex]\frac{4 - \sqrt{3} }{4 - \sqrt{3} }[/tex] = [tex]\frac{104 -26\sqrt{3} }{16 -4\sqrt{3} + 4\sqrt{3}- 3 }[/tex]
= [tex]\frac{104 - 26\sqrt{3} }{16 - 3}[/tex]
= [tex]\frac{26(4 - \sqrt{3} }{13}[/tex]
= 2(4 - [tex]\sqrt{3}[/tex])
= 8 - 4[tex]\sqrt{3}[/tex]
The required form of the given question is therefore 8 - 4[tex]\sqrt{3}[/tex]
