Question

simplify by rationalising the denominator 6+5√3÷6-5√3.

Answer 1

Hey User________

We can solve this by RATIONALIZATION METHOD....

so for resationaling we have to multiply the denominator by the conjugate if the system given....

so we get as ...


6+ 5-/3 ÷ 6- 5-/3 multiplying and dividing by 6+5-/3 in numerator and denominator..

so we know that ..,(a+b)(a-b) = a^2 - b^2 ... so applying here we get as ...


==》 (6 + 5-/3) ^2 / 6^2 - 25 ( 3)

Answer 2

$\frac{6+5\sqrt{3}}{6-5\sqrt{3}}$

Rationalising the denominator :

$\implies \frac{6+5\sqrt{3}}{6-5\sqrt{3}}\times\frac{6+5\sqrt{3}}{6+5\sqrt{3}}$

[Using the formula :

( a - b ) ( a + b ) = a² - b² ,  and

( a + b )² = a² + b² + 2 a b

$\implies \frac{(6+5\sqrt{3})^2}{(6)^2-(5\sqrt{3})^2}$ ]

$\implies \frac{36+75+60\sqrt{3}}{36-75}$

$\implies \frac{111+60\sqrt{3}}{-39}$

$\implies -\frac{3(37+20\sqrt{3}}{39}$

$\implies -\frac{(37+20\sqrt{3})}{13}$

The simplified answer is : $\boxed{-\frac{(37+20\sqrt{3})}{13}}$

Hope it helps you:-)

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