Question

8. Rationalise the denominator of
2/root 3-root 4​

Answer 1

Answer:

-(2√3+4)= -2√3-4

Step-by-step explanation:

$\frac{2}{\sqrt{3}-\sqrt{4} }$

$=\frac{2}{\sqrt{3}-2 }$

mutliply numerator and denominator by (√3+2),

$=\frac{2}{\sqrt{3}-2 } X \frac{\sqrt{3}+2}{\sqrt{3}+2}$

=$\frac{2\sqrt{3} +4}{(\sqrt{3}-2)(\sqrt{3}+2)}$

applying formula (a+b)(a-b)=a²-b² in the denominator, we get

$=\frac{2\sqrt3+4}{(\sqrt3)^{2}-2^2 }$

$=\frac{2\sqrt3+4}{3-4}$

$=\frac{2\sqrt3+4}{-1 }$

$=\frac{-(2\sqrt3+4)}{1 }$

$=-(2\sqrt3+4)$

$=-2\sqrt3-4$

HOPE IT HELPS,

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