Team Gmath Question :- Prove that √2 + √5 is irrational Solution:- Let us suppose that √2 + √5 is rational. Let , where a and b coprime integers and b ≠ 0. Now Squaring both side ⇒ √2 is rational, since is rational. This contradict the fact that √2 is an irrational number. So, our assumption … Read more
Question:- Prove that √p + √q is irrational, where p and q are primes. Solution:- Let us suppose that √p + √q is rational. Let √p + √q = a where a is rational number. ⇒ √p = a – √q On squaring both side we get ⇒ [Using formula ] The above statement is a … Read more
Exercise 1.2(Real numbers) Question 1: Prove that √5 is irrational. Solutions: Let us assume, that √5 is rational number.where, x and y are co-primes and y ≠ 0. i.e. √5 = x/y. ⇒ y√5= x Squaring both the sides, we get, (y√5)2 = x2 ⇒5y2 = x2……………………………….. (1) Thus, x2 is divisible by 5, so x is also divisible by 5. Let … Read more
Exercise 1.1(Real numbers) Exercise 1.1 real number class 10 ncert maths solutions Question 1: Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429 Solutions: (i) 140 we will get the product of its prime factor. Therefore, 140 = 2 × 2 × 5 × … Read more
Question:- Prove that 2 – √ 3 is irrational, given that √3 is irrational Solution: Let 2 – √3 be a rational number. Then there exist positive integers ‘a’ and ‘ b’, where a and b are integers having no common factor other than 1 and b ≠ 0 such that ⇒ Since a and … Read more
Question:- Prove that root 5 is an irrational number Solution:- Let us assume that on the contrary that √5 is a rational number. Then there exist positive integers ‘a’ and ‘ b’ such that ⇒ Where and are coprime i.e. there HCF is 1 Squaring both side ⇒ ⇒ is divisible by 5 then $a$ … Read more
Class 10 chapter 1(Real number) Case based 3:- Raman is hosting the new year party for his friends. He wants to purchase some eatables like patties and buns for making burgers, some towels and some shining papers and glitter papers for decorting his house. When he reaches the store, he finds that patties come in … Read more
Class 10 chapter 1(Real number) Case based 2:- The school Principal wants to address the students of classes eighth to tenth on the importance of personal hygiene. He asks the teacher in charge of the school to arrange all the students of eighth, ninth and tenth classes in a single hall. There are 84 students … Read more
Case based 1:- A seminar is being conducted by an educational organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively. (A) In each room the same number of participants are to be seated and all of them being in … Read more
Question 2: Check whether the relation R in R defined as R={(a, b): a ≤ b³} is reflexive, symmetric or transitive. Solution:- R defined as R={(a, b): a ≤ b³} is reflexive, symmetric or transitive. Reflexive:- , since is not reflexive. Symmetric:- R is not symmetric. Transitive:- is not transitive. is neither reflexive nor symmetric … Read more