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real numbers extra question 🤯🤯| class 10 | cbse 🔥🔥| hcf lcm concept

real numbers extra question 🤯🤯| class 10 | cbse 🔥🔥| hcf lcm concept #maths #youtuebe real numbers, extra questions, natural numbers, rational numbers, whole numbers, maths extra questions, class 10 chapter 1 extra question, real numbers extra questions, extra questions, maths important extra questions, cbse important questions, class 10 maths, cbse math class, maths classroom, cbse class 10 maths important video, maths by faiz sir, infinix classes, infinix classes maths, best coaching in gopalganj, gopalganj video, hcf lcm concept, maths conceptual videos, maths viral concept, viral maths concept #mathsbyfaizsir #mathsequence #mathstricks #mathspuzzle #mathsclass #realnumbers #real_numbers #real_numbers_class_10 #class10maths #class10thmaths #class_10th_math_objective_question_2025 #class_10th_trigonometry #infinixclasses #math_live_class #maths_trick #faizsir #faiz_3009 #mathsbyfaizsir Q) What is the H.C.F. of smallest prime number and the smallest composite number ? [CBSE 2018] Q) If p, q are two prime numbers then what is the HCF and LCM of p and q? Q) ‘Product of two irrational numbers is always an irrational number’. Negate the statement by giving counter Q) Show that (𝟑+ √𝟕)/𝟓 that √𝟕 is irrational.  Q) Prove that n2 + n is divisible by 2 for any positive integer n. [CBSE 2019 (C)] Q) In a school, the duration of a period in junior section is 40 minutes and in senior section is 1 hour: If the first bell for each section ring at 9:00 a.m., when will the two bells ring together again? [CBSE 2012 (Sept.)] Q) The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.[C.B.S.E Sept 2012] Q) A, B and C starts cycling around a circular path in the same direction at the same time. Circumference of the path is 1980 m. If speed of A is 330 m/min, speed of B is 198 m/min and that of C is 220 m/min and they start from the same point, then after what time will they be together at the starting point? Q) The set of Mathematics, Physics and Physical Education books have to be stacked in such a way that all the books are stored topic wise. The number of Mathematics, Physics and Physical Education books are 14, 18 and 22. Determine the number of stacks of each books provided books are of the same thickness. Q) Find the greatest number that will divide 43,91 and 183 so as to leave the same remainder in each case. Real numbers are simply the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also. At the same time, the imaginary numbers are the un-real numbers, which cannot be expressed in the number line and are commonly used to represent a complex number. Some of the examples of real numbers are 23, -12, 6.99, 5/2, π, and so on. In this article, we are going to discuss the definition of real numbers, the properties of real numbers and the examples of real numbers with complete explanations. Real Numbers Definition Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category. See the figure, given below, which shows the classification of real numerals. Set of Real Numbers The set of real numbers consists of different categories, such as natural and whole numbers, integers, rational and irrational numbers. In the table given below, all the real numbers formulas (i.e.) the representation of the classification of real numbers are defined with examples. Properties of Real Numbers The following are the four main properties of real numbers: Commutative property Associative property Distributive property Identity property Consider “m, n and r” are three real numbers. Then the above properties can be described using m, n, and r as shown below: Commutative Property If m and n are the numbers, then the general form will be m + n = n + m for addition and m.n = n.m for multiplication. Associative Property If m, n and r are the numbers. The general form will be m + (n + r) = (m + n) + r for addition(mn) r = m (nr) for multiplication. Distributive Property For three numbers m, n, and r, which are real in nature, the distributive property is represented as: m (n + r) = mn + mr and (m + n) r = mr + nr. Example of distributive property is: 5(2 + 3) = 5 × 2 + 5 × 3. Here, both sides will yield 25. Identity Property There are additive and multiplicative identities. For addition: m + 0 = m. (0 is the additive identity) For multiplication: m × 1 = 1 × m = m. (1 is the multiplicative identity)