Rationalise the denominator of the expressionfraction numerator 1 over denominator 1 plus square root of 6 minus square root of 2 end fraction

Asked by manvanthchandrashekar15.9spicertl | 10th Jun, 2020, 12:17: PM

Expert Answer:

To rationalize the given expression, we need to multiply and divide it by the conjugate of denominator.
Denominator has the number (1 + sqrt{6}) - sqrt{2}
Its conjugate will be the number (1 + sqrt{6}) + sqrt{2}
Therefore, we have
fraction numerator 1 over denominator 1 plus square root of 6 minus square root of 2 end fraction equals fraction numerator 1 over denominator open parentheses 1 plus square root of 6 close parentheses minus square root of 2 end fraction equals fraction numerator 1 over denominator open parentheses 1 plus square root of 6 close parentheses minus square root of 2 end fraction cross times fraction numerator open parentheses 1 plus square root of 6 close parentheses plus square root of 2 over denominator open parentheses 1 plus square root of 6 close parentheses plus square root of 2 end fraction
equals fraction numerator open parentheses 1 plus square root of 6 close parentheses plus square root of 2 over denominator open square brackets open parentheses 1 plus square root of 6 close parentheses minus square root of 2 close square brackets open square brackets open parentheses 1 plus square root of 6 close parentheses plus square root of 2 close square brackets end fraction
equals fraction numerator open parentheses 1 plus square root of 6 close parentheses plus square root of 2 over denominator open square brackets open parentheses 1 plus square root of 6 close parentheses squared minus open parentheses square root of 2 squared close parentheses close square brackets end fraction
equals fraction numerator open parentheses 1 plus square root of 6 close parentheses plus square root of 2 over denominator open square brackets 1 plus 6 plus 2 square root of 6 minus 2 close square brackets end fraction
equals fraction numerator open parentheses 1 plus square root of 6 close parentheses plus square root of 2 over denominator open square brackets 5 plus 2 square root of 6 close square brackets end fraction
equals fraction numerator open parentheses 1 plus square root of 6 close parentheses plus square root of 2 over denominator open square brackets 5 plus 2 square root of 6 close square brackets end fraction cross times fraction numerator 5 minus 2 square root of 6 over denominator 5 minus 2 square root of 6 end fraction space space space.... space C o n j u g a t e space o f space 5 plus 2 square root of 6 space i s space 5 minus 2 square root of 6
equals fraction numerator open square brackets open parentheses 1 plus square root of 6 close parentheses plus square root of 2 close square brackets open parentheses 5 minus 2 square root of 6 close parentheses over denominator 25 minus 4 cross times 6 end fraction
equals open square brackets open parentheses 5 plus 5 square root of 6 close parentheses plus 5 square root of 2 minus 2 square root of 6 minus 12 minus 4 square root of 3 close square brackets
equals 3 square root of 6 plus 5 square root of 2 minus 7 minus 4 square root of 3

Answered by Renu Varma | 10th Jun, 2020, 12:54: PM