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CBSE Class 10 Answered

Prove that 6 + √3 is irrational.
Asked by susrisangita792 | 06 Apr, 2023, 08:35: PM
answered-by-expert Expert Answer
To prove: 6 + √3 is irrational
Suppose 6 + √3 is a rational number.
rightwards double arrow 6 plus square root of 3 equals straight p over straight q rightwards double arrow square root of 3 equals straight p over straight q minus 6 Subtraction space of space two space rational space numbers space is space rational. rightwards double arrow open parentheses straight p over straight q minus 6 close parentheses space is space rational rightwards double arrow square root of 3 space is space straight a space rational space number comma space which space is space straight a space contradiction So comma space our space assumption space is space wrong. Thus comma space 6 plus square root of 3 space is space an space irrational space number.
Answered by Renu Varma | 10 Apr, 2023, 10:32: AM

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