Question

Rationalise

5+√2/5-√2....​

Answer 1

Answer:

Question:

• ${ \sf{Rationalise : \frac{5 + \sqrt{2} }{5 - \sqrt{2} } }}$

Solution:

$: \implies{ \sf{ \frac{5 + \sqrt{2} }{5 - \sqrt{2} } }} \\ \\ : { \implies{ \sf{ \frac{5 + \sqrt{2} }{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } }}} \\ \\ : { \implies{ \sf{ \frac{ {(5 + \sqrt{2} )}^{2} }{ {(5)}^{2} - {( \sqrt{2} )}^{2} } }}} \\ \\ : { \implies{ \sf{ \frac{ {(5)}^{2} + { \sqrt{(2}) }^{2} + 2(5)( \sqrt{2} )}{25 - 2} }}} \\ \\ : { \implies{ \sf{ \frac{25 + 2 + 10 \sqrt{2} }{23} }}} \\ \\ : { \implies{ \sf{ \frac{27 + 10 \sqrt{2} }{23} }}}$

${ \therefore{ \sf{ \frac{5 + \sqrt{2} }{5 - \sqrt{2} } = \frac{27 + 10 \sqrt{2} }{23} }}}$

Answer 2

${ \sf{ \frac{5 + \sqrt{2} }{5 - \sqrt{2} } }} \\ \\ { { \sf{ \frac{5 + \sqrt{2} }{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } }}} \\ \\ { { \sf{ \frac{ {(5 + \sqrt{2} )}^{2} }{ {(5)}^{2} - {( \sqrt{2} )}^{2} } }}} \\ \\ { { \sf{ \frac{ {(5)}^{2} + { \sqrt{(2}) }^{2} + 2(5)( \sqrt{2} )}{25 - 2} }}} \\ \\ { { \sf{ \frac{25 + 2 + 10 \sqrt{2} }{23} }}} \\ \\ { { \sf{ \frac{27 + 10 \sqrt{2} }{23} }}}$