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Rationalise the denominator of 1/√3 - √2​

Sagot :

SalmonWorldTopper

Step-by-step explanation:

[tex]\underline{\underline{\sf{➤ \:\: Solution }}}[/tex]

[tex] \sf\: \: \: \dfrac{1}{ \sqrt{3} - \sqrt{2} } [/tex]

On rationalising,

[tex] \sf \implies \dfrac{1}{ \sqrt{3} - \sqrt{2} } \times \dfrac{\sqrt{3} + \sqrt{2} }{\sqrt{3} + \sqrt{2} } [/tex]

Combine the fractions,

[tex] \sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}) } [/tex]

We know that,

[tex] \sf \implies (a - b)(a + b) = (a)^{2} - (b)^{2} [/tex]

So,

[tex] \sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{(\sqrt{3})^{2} - (\sqrt{2}) ^{2} }[/tex]

[tex] \sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{3 - 2 }[/tex]

[tex] \sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{1 }[/tex]

[tex] \sf \implies ( \sqrt{3} + \sqrt{2}) [/tex]

Hence,

On rationalising we got,

[tex]\implies \bf (\sqrt{3} + \sqrt{2}) [/tex]

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