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Prove that 6 + √3 is irrational.

Asked by susrisangita792 | 06 Apr, 2023, 08:35: PM

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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Asked by susrisangita792 | 06 Apr, 2023, 08:35: PM

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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........

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plz solve urgently dear experts Q13 tick marked :

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plz answer the TICK marked question urgently dear experts :

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