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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 | 10 Jun, 2020, 12:17: PM
answered-by-expert 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 | 10 Jun, 2020, 12:54: PM

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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 | 10 Jun, 2020, 12:17: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
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