Question

Rationalise the denominator √21/√3​

Answer 1

Question :-

Rationalise the denominator √21/√3

Solution :-

Given fraction :

• $\rm{ \frac{ \sqrt{21} }{ \sqrt{3} } }$

Rationalization

$\rm:\longmapsto{ \frac{ \sqrt{21} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } } \\ \\ \rm:\longmapsto{ \frac{ \sqrt{21} \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } } \\ \\ \rm:\longmapsto{ \frac{ \sqrt{63} }{3} } \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{ \frac{ \sqrt{7 \times 9} }{ 3 } } \: \: \:$

We know √9 = 3

$\rm:\longmapsto{ \frac{ \cancel3 \sqrt{7} }{ \cancel3} } \\ \\ \bf:\longmapsto \red{ \sqrt{7} } \:$

After rationalizing we get √7.

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