Question

rationalise the denominator 5+2√3/5-2√3​

Answer 1

Answer:

See this.

Step-by-step explanation:

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Answer 2

$\color {red} </p><p>\Large \underline {\underline {Question \: :}}$

Rationalise the denominator :

$\frac{5 + 2 \sqrt{3} }{5 - 2 \sqrt{3} }$

$\color {red} </p><p>\Large \underline {\underline {Solution \: :}}$

$= \frac{5 + 2 \sqrt{3} }{5 - 2 \sqrt{3} }$

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

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

$= \frac{25 - 12}{ {5}^{2} - 2 \times (5) \times (2 \sqrt{3}) + (2 \sqrt{3} ) {}^{2} }$

$= \frac{13}{25 - 20 \sqrt{3} + 12 }$

$= \frac{13}{37 - 20 \sqrt{3} }$

$\implies$ Hence, the answer is 13/37- 20√3.

$\color {red} </p><p>\Large \underline {\underline {Identity \: Used\: :}}$

$(a + b)(a - b) = a {}^{2} - {b}^{2}$

$(a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2}$

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