Question

rationalise the denominator of 1/√3+√2-√5

Answer 1

$\frac{1}{ (\sqrt{3} + \sqrt{2}) - \sqrt{5} }$

Rationalising Factor of[ (√3+√2)-√5]=[(√3+√2)+√5)]

Now Multiply Numerator and Denominator.

$\frac{1( \sqrt{3 + } \sqrt{2} ) + \sqrt{5} }{[( \sqrt{3} + \sqrt{2} ) - \sqrt{5}]\:[ ( \sqrt{3} + \sqrt{2}) + \sqrt{5} ]} \\ \\ \frac{( \sqrt{3} + \sqrt{2} ) + \sqrt{5} }{( \sqrt{3} + \sqrt{2} ) {}^{2} - \sqrt{5} {}^{2} } \\ \\ \frac{ \sqrt{3} + \sqrt{2} + \sqrt{5} }{3 + 2 + 2 \sqrt{3 \times 2} - 5} \\ \\ \frac{ \sqrt{3} +\sqrt{2}+ \sqrt{5} }{5 + 2 \sqrt{6} - 5 } \\ \\ \frac{ \sqrt{3} + \sqrt{2} +\sqrt{5} }{2 \sqrt{6} }$

Since √6is an Irrational Number in Denominator For Make it Rational Multiply √6with both Numerator and Denominator.

$\frac{ (\sqrt{3} + \sqrt{2}+ \sqrt{5} ) \times \sqrt{6} }{2 \sqrt{6} \times \sqrt{ 6 } } \\ \\ \frac{ \sqrt{6 \times 3} +\sqrt{6\times 2}+ \sqrt{5 \times6 } }{2 \times 6} \\ \\ \frac{ \sqrt{18} + \sqrt{12}+ \sqrt{30}}{12} \\ \\ \frac{ 3\sqrt{2} + 2\sqrt{3}+\sqrt{30}}{12}$

Answer 2

Step-by-step explanation:

rationalise the denominator of 1/√3+√2-√5