Question

5. Rationalise:
√3+√2/√3-√2​

Answer 1

$\star\:\:\:\bf\large\underline\blue{Question:-}$

• Rationalize $\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} }$

$\star\:\:\:\bf\large\underline\blue{Solution:-}$

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

$\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

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

$= \frac{3 + 2 + 2 \times \sqrt{2} \times \sqrt{3} }{1}$

$= 5 + 2 \sqrt{6}$

$\star\:\:\:\bf\large\underline\blue{Answer:-}$

• Answer for the problem is $= 5 + 2 \sqrt{6}$

Answer 2

$\bf\large\blue{Question\::-}$

• $\text{Rationalise it :-}$ $\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} }$

$\bf\large\blue{Solution\::-}$

$\text{ \underline{Steps for solving}\::-}$

• Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.

• Step 2: Make sure all radicals are simplified.

• Step 3: Simplify the fraction if needed.

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

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

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

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

$= 3 + 2 + 2 \sqrt{3 } \sqrt{2}$

$= 5 + 2 \sqrt{6}$

$\bf\large\blue{Solution\::-}$

• $\text{The rationalized denominator is}$ $= 5 + 2 \sqrt{6}$

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$\text\blue{Hope it helps you :-) }$❤️