Question

Rationalize the denominator root2/root2+root3-root5

Answer 1

Answer:

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Step-by-step explanation:

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\frac{ \sqrt{2} }{ \sqrt{2}  -   \sqrt{ 3} -  \sqrt{5}   }  \\  =  \frac{ \sqrt{2}( \sqrt{2} -  \sqrt{3} +  \sqrt{5}  )  }{( \sqrt{2}  -  \sqrt{3}  -  \sqrt{5})( \sqrt{2} -  \sqrt{3}   +  \sqrt{5} ) }  \\  =  \frac{(2 -  \sqrt{6} +  \sqrt{10})  }{ {( \sqrt{2} -  \sqrt{3})  }^{2} -  {( \sqrt{5}) }^{2}  }  \\  =  \frac{(2 -  \sqrt{6} +  \sqrt{10} ) }{(2 + 3 - 2 \sqrt{6}) - 5 }  \\  =  \frac{(2 -  \sqrt{6} +  \sqrt{10} ) }{5 - 5 - 2 \sqrt{6} }  \\  =  \frac{ -  \sqrt{6}(2 -  \sqrt{6}  +  \sqrt{10}  )}{( - 2 \sqrt{6}) \times  -  \sqrt{6}  }  \\  =  \frac{(6 - 2 \sqrt{6}  -  2 \sqrt{15}) }{12}  \\  =  \frac{1}{2}  -  \frac{ \sqrt{6} }{6}  -  \frac{ \sqrt{15} }{6}  

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