Question

Rationalise the denominator of 3/5-root3+2/5+root 3

Answer 1

Answer:

$\boxed{\sf \dfrac{25 + \sqrt{3}}{22}}$

Step-by-step explanation:

Given that ;

$\sf \frac{3}{5 - \sqrt{3} } + \frac{2}{5 + \sqrt{3} } \\ \\ \bf Taking \: LCM : \\ \\ \implies \sf \frac{3(5 + \sqrt{3} ) + 2(5 - \sqrt{3}) }{(5 - \sqrt{3} )(5 + \sqrt{3} )} \\ \\ \implies \sf \frac{15 + 3 \sqrt{3} + 10 - 2 \sqrt{3} }{(5) {}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \implies \sf \frac{25 + \sqrt{3} }{25 - 3} \\ \\ \implies \sf \frac{25 + \sqrt{3} }{22}$

Hence, the answer is $\bf \dfrac{25 + \sqrt{3}}{22}$

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$\large{\underline{\underline{\mathfrak{\heartsuit \: Algebraic \: Identity : \: \heartsuit}}}}$

• (a + b) (a - b) = a² - b²
• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab

Answer 2

Question:

Rationalise the denominator of

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

Solution:

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

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

$= \dfrac{3(5+\sqrt{3})}{25-3} + \dfrac{2(5-\sqrt{3})}{25-3}$

$= \dfrac{15+3\sqrt{3}}{22} + \dfrac{10-2\sqrt{3}}{22}$

$= \dfrac{15 + 3\sqrt{3} + 10 - 2\sqrt{3}}{22}$

$= \dfrac{25 + \sqrt{3}}{22}$

Answer

$\boxed{\dfrac{25 + \sqrt{3}}{22}}$

☆Identities used☆

• $a^{2} - b^{2} = (a + b)(a-b)$