Question

2+√3/÷2-√3) rationalise the denomnitor

Answer 1

Answer:

7 + 4√3

Step-by-step explanation:

$\dfrac{2+\sqrt3}{2-\sqrt3}$,

Divide as well as multiply by 2 + √3 :

$\implies\dfrac{(2+\sqrt3)(2+\sqrt3)}{(2+\sqrt3)(2-\sqrt3)}$

( 2 + √3 )( 2 + √3 ) = ( 2 + √3 )^2 = 2² + √3² + 2.2.√3 = 4 + 3 + 4√3 = 7 + 4√3

( 2 + √3 )( 2 - √3 ) = 2^2 - √3^2 = 4 - 3 = 1

$\implies\dfrac{7+4\sqrt3}{1}$

=> 7 + 4√3

Answer 2

$\bf \huge \red{answer : - }$

$\bf \huge \implies{7 + 4 \sqrt{3} }$

$\bf \huge \red{solution : - }$

$\bf \bold \implies \: \frac{2 + \sqrt{3} }{2 - \sqrt{3} }$

$\bf \underline\green {rationalising \: the \: denominator}$

$\bf \bold \implies \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

$\bf \bold \implies \: \frac{ {(2 + \sqrt{3}) }^{2} }{ {(2)}^{2} - {( \sqrt{3}) }^{2} }$

$\bf \bold \implies \: \frac{4 + 4 \sqrt{3} + 3}{4 - 3}$

$\bf \bold \implies \: 7 + 4 \sqrt{3}$