Question

Rationalise the denominations a) 1/root2 b) 1/root5-root2

Answer 1

Step-by-step explanation :

 $\underline{\underline{\bf Rationalizing \ factor:}}$

• The factor of multiplication by which rationalization is done, is called as rationalizing factor.

• If the product of two surds is a rational number, then each surd is a rationalizing factor to other.

• For example, rationalizing factor of (3 + √2) is (3 - √2)

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$\boxed{\bf a) \frac{1}{\sqrt{2}}}$

=>   Rationalizing factor = √2

     $= \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} \\\\\\ =\frac{\sqrt{2}}{\sqrt{2}^2} \\\\\\ =\frac{\sqrt{2}}{2}$

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$\boxed{\bf b)\frac{1}{\sqrt{5}-\sqrt{2}}}$

=>  Rationalizing factor = √5 + √2

         $=\frac{1}{\sqrt{5}-\sqrt{2}} \times \frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}+\sqrt{2}} \\\\\\ =\frac{\sqrt{5}+\sqrt{2}}{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})} \\\\\\ =\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}(\sqrt{5}+\sqrt{2})-\sqrt{2}(\sqrt{5}+\sqrt{2})} \\\\\\ =\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}^2+\sqrt{10}-\sqrt{10}-\sqrt{2}^2} \\\\\\ =\frac{\sqrt{5}+\sqrt{2}}{5-2} \\\\\\ =\frac{\sqrt{5}+\sqrt{2}}{3}$

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Answer 2

Step-by-step explanation:

Refer the attachment........