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root5+root3. proof that it is an irrational number
 
Asked by kamleshsingh826 | 23 Aug, 2016, 08:53: PM
answered-by-expert Expert Answer
begin mathsize 14px style L e t space square root of 5 plus square root of 3 space b e space r a t i o n a l space e q u a l space t o space a over b. T h e n comma space square root of 5 plus square root of 3 equals a over b rightwards double arrow square root of 5 equals a over b minus square root of 3 rightwards double arrow open parentheses square root of 5 close parentheses squared equals open parentheses a over b minus square root of 3 close parentheses squared left parenthesis S q u a r i n g space b o t h space s i d e s right parenthesis rightwards double arrow 5 equals a squared over b squared minus fraction numerator 2 a square root of 3 over denominator b end fraction plus 3 rightwards double arrow 2 equals a squared over b squared minus 2 square root of 3 a over b rightwards double arrow 2 square root of 3 a over b equals a squared over b squared minus 2 rightwards double arrow 2 square root of 3 a over b equals fraction numerator a squared minus 2 b squared over denominator b squared end fraction rightwards double arrow square root of 3 equals fraction numerator a squared minus 2 b squared over denominator 2 a b end fraction rightwards double arrow square root of 3 space i s space r a t i o n a l comma space a space c o n t r a d i c t i o n. H e n c e comma space square root of 5 plus square root of 3 space i s space i r r a t i o n a l. end style
Answered by Rashmi Khot | 24 Aug, 2016, 09:36: AM

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CBSE 10 - Maths
Prove That Root 5 Is Irrational
Asked by jilsmendapara123 | 28 Jul, 2023, 02:44: PM
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CBSE 10 - Maths
Show that 2√3 - 5 is irrational.
Asked by susrisangita792 | 24 Apr, 2023, 09:59: PM
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CBSE 10 - Maths
Prove that the following numbers are irrational: (a) 2 square root of 3 minus 4  (b) fraction numerator 1 over denominator square root of 2 end fraction  (c) square root of 3 plus square root of 5   
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Asked by susrisangita792 | 24 Apr, 2023, 03:00: PM
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CBSE 10 - Maths
Answer the following in one word, one sentence or as per the exact requirement : (a) Let p and q be two distinct prime numbers. Write HCF (p , q). (b) Fill in the blank space in the statement given below : (i) If p be a prime, then √p is _______number. (ii) If p/q is a rational number then p and q are _____ . (c) √27 is an irrational number. Justify the statement.
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Asked by susrisangita792 | 23 Apr, 2023, 09:05: AM
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CBSE 10 - Maths
Prove that 6 + √3 is irrational.
Asked by susrisangita792 | 06 Apr, 2023, 08:35: PM
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CBSE 10 - Maths
The following real numbers have decimal expansions as given below. In each case decide whether they are rational or not. If they are rational and of the form p/q write prime factors of q so that p and q are co-primes. (a) 43.123 (b) 0.120120012000........ (c) 43.123123123123........
Asked by susrisangita792 | 02 Apr, 2023, 11:51: AM
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CBSE 10 - Maths
plz solve this question urgently :
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Asked by savitamahajan202 | 30 Jan, 2023, 02:36: PM
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CBSE 10 - Maths
plz solve urgently dear experts tick marked :
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Asked by savitamahajan202 | 30 Jan, 2023, 01:57: PM
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CBSE 10 - Maths
plz solve urgently dear experts Tick marked problem :
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Asked by savitamahajan202 | 24 Jan, 2023, 12:12: PM
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CBSE 10 - Maths
plz solve urgently dear experts Q13 tick marked :
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Asked by savitamahajan202 | 24 Jan, 2023, 11:50: AM
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