Question

rationalise the denominator root3/5+2root3​

Answer 1

Answer:

$\boxed{\frac {5 \sqrt{3} - 6}{13}}$

Step-by-step explanation:

Check attachment for more explanation.

Identity used :

• Here, only one identity is used : a² - b² = (a+b) (a-b)

How to rationalize denominator?

• To rationalize denominator, we just have to change the signs i.e. + or -.
• We have to write it in the opposite side of the sum.

_______________________________

Answer 2

Rationalalise the denominator :

$\dfrac{ \sqrt{3} }{5 + 2 \sqrt{3} }$

=> $\dfrac{ \sqrt{3} }{5 + 2 \sqrt{3} } \times \dfrac{5 - 2 \sqrt{3} }{5 - 2 \sqrt{3} }$

Using the identity : (a + b)(a - b) = a² - b²

=> $\dfrac{ \sqrt{3} (5 - 2 \sqrt{3}) }{ {(5)}^{2} - {(2 \sqrt{3}) }^{2} }$

=> $\dfrac{5 \sqrt{3} - 6 }{25 - 12}$

=> $\dfrac{5 \sqrt{3} - 6 }{13}$

To rationalize a denominator, we multiply both top and bottom by changing the signs( '+' or '-' ) of the denominator.