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CBSE Class 9 Answered

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1/(√3+√5-√7)

Asked by rkjha_in | 21 Aug, 2014, 08:32: PM
answered-by-expert Expert Answer
fraction numerator 1 over denominator square root of 3 plus square root of 5 minus square root of 7 end fraction R a t i o n a l i s e space d e n o m i n a t o r comma space w e space g e t fraction numerator 1 over denominator open parentheses square root of 3 plus square root of 5 close parentheses minus open parentheses square root of 7 close parentheses end fraction cross times fraction numerator open parentheses square root of 3 plus square root of 5 close parentheses plus open parentheses square root of 7 close parentheses over denominator open parentheses square root of 3 plus square root of 5 close parentheses plus open parentheses square root of 7 close parentheses end fraction equals fraction numerator open parentheses square root of 3 plus square root of 5 close parentheses plus open parentheses square root of 7 close parentheses over denominator open parentheses square root of 3 plus square root of 5 close parentheses squared minus open parentheses square root of 7 close parentheses squared end fraction equals fraction numerator open parentheses square root of 3 plus square root of 5 close parentheses plus open parentheses square root of 7 close parentheses over denominator 3 plus 5 plus 2 square root of 15 minus 7 end fraction equals fraction numerator open parentheses square root of 3 plus square root of 5 close parentheses plus open parentheses square root of 7 close parentheses over denominator 1 plus 2 square root of 15 end fraction R a t i o n a l i s e space d e n o m i n a t o r space a g a i n equals fraction numerator open parentheses square root of 3 plus square root of 5 close parentheses plus open parentheses square root of 7 close parentheses over denominator 1 plus 2 square root of 15 end fraction cross times fraction numerator 2 square root of 15 minus 1 over denominator 2 square root of 15 minus 1 end fraction equals fraction numerator open square brackets open parentheses square root of 3 plus square root of 5 close parentheses plus open parentheses square root of 7 close parentheses close square brackets cross times open square brackets 2 square root of 15 minus 1 close square brackets over denominator 59 end fraction equals 1 over 59 open square brackets 6 square root of 5 minus square root of 3 plus 10 square root of 3 minus square root of 5 plus 2 square root of 135 minus square root of 7 close square brackets equals 1 over 59 open square brackets 5 square root of 5 plus 9 square root of 3 plus 2 square root of 135 minus square root of 7 close square brackets
Answered by Dharma Teja | 22 Aug, 2014, 08:52: AM

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