[-7\sqrt{3}+14] Rationalise the denominaor in \dfrac{7}{\sqrt{3}+2}

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Aptitude

TNPSC G4

10th CBSE Maths

Rationalise the denominaor in $\dfrac{7}{\sqrt{3}+2}$

$-7\sqrt{3}+14$

$7\sqrt{3}+14$

$-7\sqrt{3}-14$

$7\sqrt{3}-14$

Explanation:
$\dfrac{7}{\sqrt{3}+2}=\dfrac{7}{\sqrt{3}+2} \times \dfrac{\sqrt{3}-2}{\sqrt{3}-2}$ [multiply the numerator and denominator by $\sqrt{3}-2$]

=$\dfrac{7\sqrt{3}-14}{3-4}$

=$\dfrac{7\sqrt{3}-14}{-1}$

=$-7\sqrt{3}+14$

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