Question

Q1.Rationalise the denominator
(i) 1/√7 (ii) 1/√7-√6
(iii) 1/√5+√2 (iv) 1/√7-2​

Answer 1

Explanation:

$(i) \sf \dfrac{1}{\sqrt{7}} </p><p>$

$\longrightarrow \sf \dfrac{1}{\sqrt{7}} \times \dfrac{\sqrt{7}}{\sqrt{7}}$

$\longrightarrow \pmb{\sf \dfrac{\sqrt{7}}{7}}$

Hence, Rationalised!!

$(ii) \sf \dfrac{1}{\sqrt{7} - \sqrt{6}} </p><p>$

$\longrightarrow \sf \dfrac{1}{\sqrt{7}-\sqrt{6}} \times \dfrac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}}$

$\longrightarrow \sf \dfrac{\sqrt{7}+\sqrt{6}}{(\sqrt{7})^{2}-(\sqrt{6})^{2}}$

$\longrightarrow \sf \dfrac{\sqrt{7}+\sqrt{6}}{7-6}</p><p> </p><p> </p><p>$

$\longrightarrow \sf \dfrac{\sqrt{7}+\sqrt{6}}{1}$

$\longrightarrow \pmb{\sf \sqrt{7}+\sqrt{6}}$

Hence, Rationalised!!

$(iii) \sf \dfrac{1}{\sqrt{5} + \sqrt{2}} </p><p>$

$\longrightarrow \sf \dfrac{1}{\sqrt{5} + \sqrt{2}} \times \dfrac{\sqrt{5}-\sqrt{2}}{\sqrt{5} - \sqrt{3}}$

$\longrightarrow \sf \dfrac{\sqrt{5 }- \sqrt{2}}{(\sqrt{5})^{2}- (\sqrt{2})^{2}}$

$\longrightarrow \sf \dfrac{\sqrt{5}- \sqrt{2}}{5-2}$

$\longrightarrow \pmb{\sf \dfrac{\sqrt{5}-\sqrt{2}}{3}}$

Hence, Rationalised!!

$(iv) \sf \dfrac{1}{\sqrt{7} - 2} </p><p>$

$\longrightarrow \sf \dfrac{1}{\sqrt{7} - 2} \times \dfrac{\sqrt{7} + 2}{\sqrt{7}+2}$

$\longrightarrow \sf \dfrac{\sqrt{7} + 2}{(\sqrt{7})^{2}-(2)^{2}}$

$\longrightarrow \sf \dfrac{\sqrt{7} + 2}{7-4}$

$\longrightarrow \pmb{\sf \dfrac{\sqrt{7} + 2}{3}}$

Hence, Rationalised!!

Identity used :-

(a + b) (a - b) = a² - b²