2.5.1 Show that there can be no rational number which is the square root of 2....

Transcribed Image Text:

2.5.1 Show that there can be no rational number which is the square root of 2. (Hint: Start by assuming that there is such a number, and observe that if it does exist it can be expressed as a fraction in lowest terms. From this starting point, show that both the numerator and the denominator of the fraction are necessarily divisible by two, and thus the fraction, which was assumed to be in lowest terms, is not in lowest terms and can not be put in lowest terms. Therefore, the initial assumption, that the fraction exists, must be false.) 2.5.1 Show that there can be no rational number which is the square root of 2. (Hint: Start by assuming that there is such a number, and observe that if it does exist it can be expressed as a fraction in lowest terms. From this starting point, show that both the numerator and the denominator of the fraction are necessarily divisible by two, and thus the fraction, which was assumed to be in lowest terms, is not in lowest terms and can not be put in lowest terms. Therefore, the initial assumption, that the fraction exists, must be false.)

Answer rating: 100% (QA)

Answer Then Suppose where f and They gcd but 22q q are P 9 1 P ... View the full answer