Question

5-√3/5+√3 rationalise the denominator

Answer 1

Answer:

1 please mark me as brainliest if possible

Step-by-step explanation:

5-√3/5+√3= (5-√3/5+√3)×(5-√3/5-√3)

(5-√3)^2/5^2-√3^2

25-3/25-3

1/1

1

Answer 2

Answer:

$\longmapsto \tt \dfrac{14-5\sqrt{3}}{11}$

Step-by-step explanation:

$\longmapsto \tt \dfrac{5-\sqrt{3}}{5+\sqrt{3}}$

Rationalizing factor = 5 - √3

Multiply and divide the fraction by the rationalizing factor,

$\longrightarrow \tt \dfrac{5-\sqrt{3}}{5+\sqrt{3}} \times \dfrac{5-\sqrt{3}}{5-\sqrt{3}} \\\\\\ \longrightarrow \tt \dfrac{(5-\sqrt{3})^2}{(5+\sqrt{3})(5-\sqrt{3})} \\\\\\ \longrightarrow \tt \dfrac{5^2+(\sqrt{3})^2-2(5)(\sqrt{3})}{5^2 - \sqrt{3}^2}$

Identities used :

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

$\longrightarrow \tt \dfrac{25+3-10\sqrt{3}}{25-3} \\\\ \longrightarrow \tt \dfrac{28-10\sqrt{3}}{22} \\\\ \longrightarrow \tt \dfrac{2(14-5\sqrt{3})}{2(11)} \\\\ \longrightarrow \tt \dfrac{14-5\sqrt{3}}{11}$