Question

Rationalizing :-
• 1/√7
• 1/√5+√2
• 1/ √7-2

Answer 1

✍️Question :-

Rationalise the following :-

$\red \mapsto \sf \frac{1}{ \sqrt{7} }$

$\red \mapsto \sf \frac{1}{ \sqrt{5} + \sqrt{2} }$

$\red \mapsto \sf \frac{1}{ \sqrt{7} - 2 }$

✍️Solution :-

$\red \mapsto \sf \frac{1}{ \sqrt{7} }$

$\green \mapsto \sf \frac{1}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} }$

$\green \mapsto \sf \frac{ \sqrt{7} }{7}$

$\red \mapsto \sf \frac{1}{ \sqrt{5} + \sqrt{2} }$

$\green \mapsto \sf \frac{1}{ \sqrt{5} + \sqrt{2} } \times \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} }$

☃️Using the identity :-

$\sf (a-b)(a+b)=a^2-b^2$

$\green \mapsto \sf \frac{ \sqrt{5} - \sqrt{2} }{( \sqrt{5} )^2-( \sqrt{2} )^2}$

$\green \mapsto \sf \frac{ \sqrt{5} - \sqrt{2} }{5-2}$

$\green \mapsto \sf \frac{ \sqrt{5} - \sqrt{2} }{3}$

$\red \mapsto \sf \frac{1}{ \sqrt{7} - 2}$

$\green \mapsto \sf \frac{1}{ \sqrt{7} -2} \times \frac{ \sqrt{7} + \sqrt{2} }{ \sqrt{7} + \sqrt{2} }$

☃️Using the identity :-

$\sf (a+b)(a-b)=a^2-b^2$

$\green \mapsto \sf \frac{ \sqrt{7} + 2}{( \sqrt{7})^2-(2)^2 }$

$\green \mapsto \sf \frac{ \sqrt{7} + 2}{7-4}$

$\green \mapsto \sf \frac{ \sqrt{7} +2 }{3}$

Answer 2

$\huge \sf \color{Blue}\underline{\underline{Question}}$

$\large ✯ \sf \frac{1}{√7}$

$\large ✯ \sf \frac{1}{ \sqrt{5} + \sqrt{2} }$

$\large ✯ \sf \frac{1}{ \sqrt{7} - 2}$

$\color{red} ━━━━━━━━━━━━━━━━━━━━━━━━━━$$\color{red} ━━━━━━━━━━━━━━━━━━━━━━━━━━$

$\huge \sf \color{Blue}\underline{\underline{Solution}}$

$\huge✯ \color{green} \sf \frac{1}{√7}$

$\large \sf ⟹\frac{1}{√7}×\frac{√7}{√7}\\ \large \sf \frac{√7}{7}$

$\color{red} ━━━━━━━━━━━━━━━━━━━━━━━━━━$

$\huge ✯ \color{green}\sf \frac{1}{ \sqrt{5} + \sqrt{2} }$

$⟹ \sf \frac{1}{ \sqrt{5} + \sqrt{2} } \times \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} }$

$⟹ \sf \frac{ \sqrt{5} - \sqrt{2} }{( \sqrt{5} )^2-( \sqrt{2} )^2}\\ \\⟹\frac{√5-√2}{5-2} \\ \\ ⟹ \frac{√5-√2}{3}$

$\color{red} ━━━━━━━━━━━━━━━━━━━━━━━━━━$

$\huge ✯\color{green} \sf \frac{1}{ \sqrt{7} - 2}$

$⟹ \sf \frac{1}{√7-2}×\frac{√7+2}{√7+2}\\ \\ ⟹ \sf \frac{√7+2}{√7²-2²} \\ \\⟹ \sf\frac{√7+2}{7-4}\\ \\ ⟹ \sf\frac{√7+2}{3}$

$\color{red} ━━━━━━━━━━━━━━━━━━━━━━━━━━$$\color{red} ━━━━━━━━━━━━━━━━━━━━━━━━━━$