Question

rationalize √3-1/√3+1​

Answer 1

Step-by-step explanation:

Hop.e it he.lps u.hh.

Ple.ase fo.llow m.e.

Answer 2

Answer:

Question:

${ \sf{Rationalize : \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} }}$

Solution:

Rationalizing the denominator;

$: { \implies{ \sf{ \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } }}} \\ \\ : { \implies{ \sf{ \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } \times \frac{ \sqrt{3} - 1 }{ \sqrt{3} - 1} }}} \\ \\ : { \implies{ \sf{ \frac{ {( \sqrt{3} - 1)}^{2} }{ { \sqrt{3} }^{2} - {1}^{2} } }}} \\ \\ : { \implies{ \sf{ \frac{ { (\sqrt{3} )}^{2} + {1}^{2} - 2( \sqrt{3}) (1)}{3 - 1} }}} \\ \\ : { \implies{ \sf{ \frac{3 + 1 - 2 \sqrt{3} }{2} }}} \\ \\ : { \implies{ \sf{ \frac{4 - 2 \sqrt{3} }{ 2} }}} \\ \\ : { \implies{ \sf{ \frac{2(2 - \sqrt{3}) }{2} }}} \\ \\ : { \implies{ \sf{2 - \sqrt{3} }}}$

Used formulae:

• (a - b) ² = a² + b² - 2ab
• a² - b² = (a + b) (a - b)