Question

Rationalise the denominator of √2+√5/√2-√5​

Answer 1

see the image and let me know if you understand

Answer 2

✪  $\huge{\underline{\overline{\mathbf{Question}}}}$  ✪

→Rationalise the denominator of √2+√5/√2-√5

✪  $\huge{\underline{\overline{\mathbf{Answer}}}}$  ✪

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

⇒$\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}-\sqrt{5}}\times \frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}+\sqrt{5}}$

⇒$\frac{(\sqrt{2}+\sqrt{5})^2}{(\sqrt{2}-\sqrt{5})(\sqrt{2}+\sqrt{5})}$

⇒$\frac{(\sqrt{2}+\sqrt{5})^2}{(\sqrt{2})^2-(\sqrt{5})^2}$

⇒$\frac{(\sqrt{2})^2+(\sqrt{5})^2+2\sqrt{10}}{2-5}$

⇒$\frac{2+5+2\sqrt{10}}{-3}$

⇒$\huge{\pink{\frac{-(7+2\sqrt{10})}{3}}}$

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Formulas Used :-

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

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