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CBSE Class 10 Answered

Show that 2√3 - 5 is irrational.
Asked by susrisangita792 | 24 Apr, 2023, 09:59: PM
answered-by-expert Expert Answer
To prove: 2√3 - 5 is irrational
Suppose 2√3 - 5 is rational
rightwards double arrow 2 square root of 3 minus 5 equals straight p over straight q
rightwards double arrow 2 square root of 3 equals straight p over straight q plus 5
rightwards double arrow square root of 3 equals fraction numerator begin display style straight p over straight q end style plus 5 over denominator 2 end fraction
Addition space of space two space rational space numbers space is space straight a space rational space number
rightwards double arrow straight p over straight q plus 5 space is space rational
rightwards double arrow fraction numerator straight p over straight q plus 5 over denominator 2 end fraction space is space rational
rightwards double arrow square root of 3 space is space rational
Which space is space straight a space contradiction.
Hence comma space 2 square root of 3 minus 5 space is space an space irrational space number.
Answered by Renu Varma | 25 Apr, 2023, 09:43: AM
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