Question

Rationalise the denominator and simplify
(a)1/7+4√3
(b)5/3+√5​

Answer 1

Answer:

(a) 7 - 4√3

(b) (15 - 5√5)/4

Step-by-step explanation:

(a)

$\frac{1}{7+4\sqrt{3} } \\\\\frac{1}{7 + 4\sqrt{3} } *\frac{7-4\sqrt{3} }{7 - 4\sqrt{3} } \\\\\frac{7 - 4\sqrt{3}}{(7^{2} - (4\sqrt{3} )^{2})} \\\\\frac{7 - 4\sqrt{3}}{49-48} \\\\\frac{7 - 4\sqrt{3}}{1} \\\\7 - 4\sqrt{3}$

(b)

$\frac{5}{3+\sqrt{5} } \\\\\frac{5}{3+\sqrt{5} } *\frac{3-\sqrt{5}}{3-\sqrt{5}} \\\\\frac{5(3-\sqrt{5})}{3^{2}-(\sqrt{5} )^{2} } \\\\\frac{15-5\sqrt{5} }{9-5} \\\\\frac{15-5\sqrt{5} }{4}$