Question

Rationalise the denominator and simplify.​

Answer 1

Answer

• 7 + 5√2

$\orange{\bigstar}$  Given  $\green{\bigstar}$

$\bullet \;\; \rm \dfrac{1+\sqrt{2}}{3-2\sqrt{2}}$

$\orange{\bigstar}$  To Find  $\green{\bigstar}$

Simplified value of the given

$\orange{\bigstar}$  Solution  $\green{\bigstar}$

$\rm \dfrac{1+\sqrt{2}}{3-2\sqrt{2}}$

Rationalize the denominator ,

$\to \rm \dfrac{1+\sqrt{2}}{3-2\sqrt{2}}\times \dfrac{3+2\sqrt{2}}{3+2\sqrt{2}}\\\\\to \rm \dfrac{(1+\sqrt{2})(3+2\sqrt{2})}{(3)^2-(2\sqrt{2})^2}\\\\\bf \because\ (a+b)(a-b)=a^2-b^2\\\\\to \rm \dfrac{3+2\sqrt{2}+3\sqrt{2}+4}{9-8}\\\\\to \rm 3+5\sqrt{2}+4\\\\\to \rm 7+5\sqrt{2}\ \; \bigstar$

Answer 2

Answer:

$\huge\bigstar\:\underline{\boxed{\tt \: 7 + 5 \sqrt{2}} } \: \bigstar$

Step-by-step explanation:

$:\implies\:\tt \dfrac{1 + \sqrt{2}}{3 - 2 \sqrt{2}}$

$:\implies\:\tt \dfrac{1 + \sqrt{2}}{3 - 2 \sqrt{2}} \: \times \: \sf \dfrac{3 + 2 \sqrt{2}}{3 - 2 \sqrt{2}}$

$:\implies\:\tt \dfrac{3 + 2\sqrt{2} \: + \: 3 \sqrt{2} \: + \: 2 \sqrt{4} }{(3)^{2} - (2\sqrt{2})^{2} }$

$:\implies\:\tt \dfrac{3 + 5\sqrt{2} \: + \: 2 \: \times \: \sqrt{2 \: \times \: 2} }{9 \: - \: 4\: \times \: 2 }$

$:\implies\:\tt \dfrac{3 \: + \: 5\sqrt{2} \: + \: 2 \: \times \: 2 }{9 \: - \: 4 \: \times \: 2 }$

$:\implies\:\tt \dfrac{3 \: + \: 5\sqrt{2} \: + \: 4 }{9 \: - \: 8}$

$:\implies\:\tt \dfrac{3 \: + \: 5\sqrt{2} \: + \: 4 }{1}$

$: \implies {\underline{\boxed{\tt \: \: 7 + 5 \sqrt{2}}} } \:\:\:\:\:\bigg \lgroup \: \bf{Required \: Answer} \: \bigg \rgroup$