Question

1) Rationalise the denomination of 5/√3-√5

2) Rationalise the denomination of 1/7+3√2​

Answer 1

${ \bf{ \underline{Question \: (1)}}}$

$↦ \: \frac{5}{ \sqrt{3} - \sqrt{5} }$

${ \bf{ \underline{Solution \: (1)}}}$

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

$= \frac{5( \sqrt{3} + \sqrt{5} }{3 - 5}$

$= ( \frac{ - 5}{2} ) \: ( \sqrt{3} + \sqrt{5} )$

${ \bf{ \underline{Question \: (2)}}}$

$↦ \: \frac{1}{7 + 3 \sqrt{2} }$

${ \bf{ \underline{Solution \: (2)}}}$

$\frac{1}{7 + 3 \sqrt{2} } = \frac{1}{7 + 3 \sqrt{2} } \times ( \frac{7 - 3 \sqrt{2} }{7 - 3 \sqrt{2} } )$

$= \frac{7 - 3 \sqrt{2} }{49 - 18} = \frac{7 - 3 \sqrt{2} }{31}$

_______________________________

Answer 2

1.

☆ $\sf{Question :-}$

➺ $\: \frac{5}{ \sqrt{3} - \sqrt{5} }$

☆ $\sf{Solution :-}$

➺ $\: \frac{5}{ \sqrt{3} - \sqrt{5} }$ = $\: \frac{5}{ \sqrt{3} - \sqrt{5} }$ × $\: \frac{ \sqrt{3} + \sqrt{5}}{ \sqrt{3} + \sqrt{5} }$

➺ $\frac{5( \sqrt{3} + \sqrt{5)} }{3 - 5}$

➺ $( \frac{ - 5}{2} ) \: ( \sqrt{3} + \sqrt{5} )$ $\mathrm\purple{[Answer]}$

2.

☆ $\sf{Question :-}$

➺ $\: \frac{1}{7 + 3 \sqrt{2} }$

☆ $\sf{Solution :-}$

➺ $\frac{1}{7 + 3 \sqrt{2} } = \frac{1}{7 + 3 \sqrt{2} } \times ( \frac{7 - 3 \sqrt{2} }{7 - 3 \sqrt{2} } )$

➺ $\frac{7 - 3 \sqrt{2} }{49 - 18} = \frac{7 - 3 \sqrt{2} }{31}$ $\mathrm\pink{[Answer]}$