Witryna19 lis 2009 · Because b is rational, there exist integers p and q such that b=p/q. Consider a+b. a+b= (m/n)+ (p/q)= (mq/nq)+ (pn/mq)= (mq+pn)/ (nq). (mq+pn) is an integer because the product of two integers... WitrynaCedric is a versatile and experienced start-up professional with a proven track record of success in driving business efficiency and innovation. He possesses a clear and rational vision and a determination to overcome challenges, which enables him to consistently achieve his goals. With a thirst for knowledge and an ability to quickly grasp …
2.1: Propositions - Mathematics LibreTexts
Witryna1 gru 2024 · The answer is integer. The product or answer of two rationals is like getting or multiplying two fractions, which will have another fraction of this similar form as the outcome since integers are sealed under multiplication. All rational number can be indicated as q/r, with q and r are equally integers. WitrynaCLAIM: the square root of a non prime number is rational Take 8 for example. 8 is not prime, correct. But, √8 = √4·√2 = 2·√2. Now the 2 in √2 is prime and therefore the square root of it IS irrational, and an irrational number times a rational number is ALWAYS irrational. Yikes! we have found one non-prime number whose square root is irrational. gwyn thomas gododdin
Can the product of two irrational numbers be rational ... - Brainly
Witryna12 maj 2016 · The square root of ab can be sometimes rational, sometimes irrational. let us take two example 1) suppose a = 1/9 b = 1/4 ab = 1/36 √ab = 1/6 (also a rational number) 2) suppose a = 1/5 b = 1/2 ab = 1/10 ab = 1/√10 ( an irrational number) Therefore, The difference between a and b is always rational. The product of a and … Witryna11 lis 2024 · All rational number can be signified as q/r, with q and r are both integers. Another explanation is the product of two rational numbers is q/r * s/t, with q, r, s, and t are integers. Nonetheless, this is just (qs)/ (rt), and qs and rt are both results of integers and hence integers themselves. Witryna4 sie 2024 · For all integers a, b, and d with d ≠ 0, if d divides a or d divides b, then d divides the product ab. Hint: Notice that the hypothesis is a disjunction. So use two cases. (b) Write the contrapositive of the proposition in Exercise (5a). (c) Write the converse of the proposition in Exercise (5a). Is the converse true or false? gwyn thomas footballer