Question

rationalise the denominator 1/root3+root5+root7

Answer 1

Answer:

-1(√3-√5-√7) /9

Step-by-step explanation:

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Answer 2

Rationalization is a defense mechanism in which apparent logical reasons are given to justify behavior that is motivated by unconscious instinctual impulses. It is an attempt to find reasons for behaviors, especially ones own.

mathematics : the part of a fraction that is below the line and that functions as the divisor of the numerator.

In elementary algebra, root rationalisation is a process by which radicals in the denominator of an algebraic fraction are eliminated.

$\frac{1}{\sqrt{3}+\sqrt{5} +\sqrt{7} }$

Conjugate of ${\sqrt{3}+\sqrt{5} +\sqrt{7} } ={\sqrt{3}-\sqrt{5} -\sqrt{3} }$

$=\frac{1({\sqrt{3}-\sqrt{5} -\sqrt{7} } )}{({\sqrt{3}+\sqrt{5} +\sqrt{7} } )({\sqrt{3}-\sqrt{5} -\sqrt{7} } )}$

$=\frac{{\sqrt{3}-\sqrt{5} -\sqrt{7} } }{\sqrt{3}({\sqrt{3}-\sqrt{5} -\sqrt{7} } )+\sqrt{5}({\sqrt{3}-\sqrt{5} -\sqrt{7} } )+\sqrt{7} ({\sqrt{3}-\sqrt{5} -\sqrt{7} } ) }$

$=\frac{{\sqrt{3}-\sqrt{5} -\sqrt{7} } }{3-\sqrt{15}-\sqrt{21}+\sqrt{15}-5-\sqrt{35}+\sqrt{21}+\sqrt{35}-7 }$

$=\frac{{\sqrt{3}-\sqrt{5} -\sqrt{7} } }{3-5-7} =\frac{{\sqrt{3}-\sqrt{5} -\sqrt{7} } }{-9}$

$=\frac{-1({\sqrt{3}-\sqrt{5} -\sqrt{7} } )}{9}$

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