Question

Rationalise the denominator of each of the following ( 1 - 9)​

Answer 1

Answer:

11 - 16√3

Step-by-step explanation:

To Rationalize :-

$\bf\dfrac{5+2\sqrt{3}}{7+4\sqrt{3}}$

Solution :-

$\bf\dfrac{5+2\sqrt{3}}{7+4\sqrt{3}}$

Multiplying and dividing with Rationlising factor " 7 - 4√3 " :-

[ So that there will be no change in the number ]

$\bf=\dfrac{5+2\sqrt{3}}{7+4\sqrt{3}}\times \dfrac{7-4\sqrt{3}}{7-4\sqrt{3}}$

$=\bf\dfrac{(5+2\sqrt{3})\times 7-4\sqrt{3}}{7+4\sqrt{3}\times 7-4\sqrt{3}}$

$=\bf\dfrac{5(7-4\sqrt{3})+2\sqrt{3}(7-4\sqrt{3})}{(7)^2-(4\sqrt{3})^2}$

$=\bf\dfrac{35-20\sqrt{3}+14\sqrt{3}-8(3)}{49-16(3)}$

$=\bf\dfrac{35-16\sqrt{3}-24}{49-48}$

$=\bf\dfrac{11-16\sqrt{3}}{1}$

= 11 - 16√3

Know More :-

Rationalising factor of :-

1. 11 - 6√3 = 11 + 6√3

2. √6 = √6

3. 2√7 = √7