Question

rationalize the denominators​

Answer 1

Given :

• 1 / √3 - √2

To Find :

• Rationalize the denominator .

Solution :

$\longmapsto\tt\bf{\dfrac{1}{\sqrt{3}-\sqrt{2}}}$

$\longmapsto\tt{\dfrac{1}{\sqrt{3}-\sqrt{2}}\times\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}}$

Using Identity : (a-b) (a+b) = a² - b² :

$\longmapsto\tt{\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{(3)}^{2}-\sqrt{(2)}^{2}}}$

$\longmapsto\tt{\dfrac{\sqrt{3}+\sqrt{2}}{3-2}}$

$\longmapsto\tt\bf{\dfrac{\sqrt{3}+\sqrt{2}}{1}}$

So , The Final Answer is √3 + √2 /1 ...

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Some More Identities :

$\begin{gathered}\begin{gathered}\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}\end{gathered}\end{gathered}$