Question

Rationalize the denominator 2/√3-√2

Answer 1

Answer:

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Answer 2

Given :–

• A fraction, $\dfrac{2}{\sqrt{3} - \sqrt{2}}$

Required :–

• Rationalise the denominator.

Solution :–

The given fraction is, $\dfrac{2}{\sqrt{3} - \sqrt{2}}$

Now, multiply the additive inverse of the denominator by both the denominator and the numerator.

⟹ $\dfrac{2}{ \sqrt{3} - \sqrt{2} } \times \dfrac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

Now, multiply this, we get,

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

⟹ $\dfrac{2( \sqrt{3} + \sqrt{2}) }{3 - 2}$

⟹ $\dfrac{2( \sqrt{3} + \sqrt{2} )}{1}$

⟹ 2(√3 + √2)

Hence,

The answer is 2(√3 + √2)