Question

Rationalise the number:

A) 5/2+√3
B) 8/ √5-√6
C) 3/√5​

Answer 1

Answer:

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Answer 2

A)

$\frac{5}{2 + \sqrt{3} }$

$= \frac{5}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$= \frac{10 - 5 \sqrt{3} }{4 - 3} \\ \\ = \frac{10 - 5 \sqrt{3} }{1} \\ \\ = 10 - 5 \sqrt{3}$

B)

$\frac{8}{ \sqrt{5} - \sqrt{6} }$

$= \frac{8}{ \sqrt{5} - \sqrt{6} } \times \frac{ \sqrt{5} + \sqrt{6} }{ \sqrt{5} + \sqrt{6} }$

$= \frac{8 \sqrt{5} + 8 \sqrt{6} }{5 - 6} \\ \\ = \frac{8 \sqrt{5} + 8 \sqrt{6} }{ - 1} \\ \\ = - 8 \sqrt{5} - 8 \sqrt{6}$

C)

$\frac{3}{ \sqrt{5} } \\ \\ = \frac{3}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } \\ \\ = \frac{3 \sqrt{5} }{5}$