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NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers NCERT solutions for class 10 maths chapter 1 � Real Numbers Exercise is the fourth exercise of Chapter 1 of class 10 Maths. After introducing Real Numbers in Class 9, it is discussed in further detail in Class In this class, It explains the rational numbers and their decimal expansions. The exercise discusses when exactly the decimal expansion of a rational number is terminating and when it is non . Access Answers of Maths NCERT Class 10 Chapter 1 � Real Number Exercise 1. Express each number as a product of its prime factors: (i) (ii) (iii) (iv) (v) Solutions: (i) By Taking the LCM of , we will get the product of its prime . Access Answers of Maths NCERT Class 10 Chapter 1 � Real Number Exercise 1. Prove that v 5 is irrational. Solutions: Let us assume, that v 5 is rational number. i.e. v 5 = x/y (where, x and y are co-primes) y v 5= x. Squaring both the sides, we get, (y v 5) 2 = x 2. ?5y 2 = x 2 .
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Alternatively: Let Real Numbers Class 10th Ncert Solutions System n be the number of columns such that the value of n be maximum and it must divide both the numbers and Alternatively: Let a be a positive integer, q be the quotient and r be the remainder. Hence, proved. Let a be a positive integer, q be the quotient and r be the remainder. Question 1: Express each number as a product of its prime factors: i ii iii iv v Solution:.

Question 5: Check whether 6 n can end with the digit 0 for any natural number n. So, there is no natural number VT for which 6 n ends with the digit zero. Solution: Method 1: Both N 1 and N 2 are expressed as a product of primes. Therefore, both are composite numbers. Question 7: There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of Ncert Solutions Class 10th Real Numbers Ed the field, while Ravi takes 12 minutes for the same.

Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Solution: Method By taking LCM of time taken in minutes by Sonia and Ravi, we can get the actual number of minutes after which they meet again at the starting point after both start at same point and of the same time, and go in the same direction. Question 1. Solution: Let us assume that is rational. But this contradicts the fact that a and b are co-primes. Thus, 5 is a common factor of both p and q. Question 2. But, it is a contradiction. Question 3.

Prove that the following are irrational. Hence proved. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? Rational numbers and irrational numbers are taken together form the set of real numbers.

The set of real numbers is denoted by R. Thus every real number is either a rational number or an irrational number. In either case, it has a non�terminating decimal representation. In the case of rational numbers, the decimal representation is repeating including repeating zeroes and if the decimal representation is non�repeating, it is an irrational number.

From the above discussion we may conclude that: To every real number there corresponds a unique point on the number line and conversely, to every point on the number line there corresponds a real number.

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