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All numbers can be classified into two categories -- Real and Imaginary. A real number can be actually perceived and can be represented in a number line. It includes Class 10 Maths Ch 5 Extra Questions 2?? all integers -- positive and negative, all natural numbers 1, 2, 3, �. An imaginary number on the other hand cannot be perceived. Square root of all negative numbers is imaginary.

A real number can be represented as an infinite decimal expansion. A real number can be rational or irrational. All rational numbers and all irrational numbers together make a group of real numbers.

A rational number an be written in the form p qboth p and q being integers q 0 while an irrational number can not be impressed in such a way. The decimal expansion of a rational number say x can terminate after a finite number of digits.

On the other hand in case of an irrational number, the decimal expansion continues without repeating. Ex: 1. First, let us understand the meaning of Lemma and Algorithms. A Lemma is a minor proven statement which is used to prove other statements. An algorithm means a series of well defined steps, which provides a procedure of calculations repeatedly successfully on the results of earlier steps. With the help of defined procedure the desired result can be obtained.

F Highest Common Factor of the ch 1 class 10 maths important questions with positive integers. Ordinarily, if we want to find the HCF of two positive integers, we first find the factors of the two integers. For ex: For two integers 24 and 42, the common factors are 1, 2, 3 and 6. As 6 is the highest of other numbers, 6 is the HCF of 24 and Next the smaller integer is divided by the above remainder and the process is repeated till zero is obtained.

The remainder in the last but one division is the required HCF. According to this theorem every positive integer is either a prime number or it can be expressed as the product of primes. It is also known as Unique Factorization Theorem. Thus, any integer that is greater than 1 can be either a prime number or can be expressed as a product of prime factors.

Note :. It is the only number that is both prime and. A chain of factors that is demonstrated in the form of ch 1 class 10 maths important questions with tree, is called Ch 3 Maths Class 10 Extra Questions Vba a factor tree. HCF is the product of the smallest power of each common prime factor present in the numbers. The product of the largest power of each prime factor present in the numbers is the LCM.

Important Note:. We use the method of contradiction in order to prove irrationality of the numbers. If a prime number p divides a 2then p divides a, where a is a positive integer.

Let us understand how to write the decimal expansion of those rational numbers with terminating decimal expansion. The important questions for this chapter is basically a compilation of higher and more advanced techniques a student can expect in Class 10 examinations. The questions of the chapter and the notes related to the topic provided by Vedantu will not only help you to understand the concept better but also solve the questions successfully.

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Vedantu provides abundant solutions and study materials for students from all the curriculums of the country. These solutions, notes and study materials not only give you enough practice ch 1 class 10 maths important questions with the exams but also boost your confidence and strengthen your conceptual understanding of the subject.

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Apr 30, �� Important questions for Class 10 Maths Chapter 1, Real Numbers is prepared by experts of Vedantu with a purpose of creating important questions for the chapter is to enable the students to pivotal concepts of the chapter that has been introduced in Maths . CBSE Class 10 Maths Chapter-1 Real Numbers Important Questions � Free PDF Download. Free PDF download of Important Questions with Answers for CBSE Class 10 Maths Chapter 1 � Real Numbers prepared by expert Maths teachers from latest edition of CBSE(NCERT) books only by CoolGyan to score more marks in CBSE board examination. Dec 28, �� CBSE Class 10 Maths Important Questions Chapter 1 � Real Numbers 1 Mark Questions 1. Use Euclid�s division lemma to show that the square of any positive integer is either of form 3m or 3m + 1 for some integer m.

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