Question

rationalize the(√5-√2)(√5+√2)​

Answer 1

Answer:

$\frac{7-2\sqrt{10} }{3}$

Step-by-step explanation:

To Rationalise:-

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

Rationalisation:-

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

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

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

$\frac{5+2-2\sqrt{10} }{5-2}$

$\frac{7-2\sqrt{10} }{3}$

Some Formulas to Remember which are applied during Rationalisation:-

(a-b)²=a²-2ab+b²

(a)²-(b)²=(a+b)(a-b)