Check whether 5 .27 41 ¯ is an irrational number or not.

An irrational number is a number that is non - terminating and non - repeating. 5 .27 41 ¯ = 5 . 274141 . . . . . . . which is a non -terminating, repeating decimal, and hence is rational.

Prove that ( 2 + 3 ) is irrational.

If possible, let ( 2 + 3 ) be rational. Then 2 and 3 are rational. ⇒ 2 + 3 − 2 is rational .... ( ∵ difference of two rationals is rational) ⇒ 3 is rational This contradicts the fact that 3 is irrational. The contradiction arises by a assuming that ( 2 + 3 ) is rational. Hence, 2 + 3 is irrational.

Find the HCF and LCM of 8 9 , 10 27 and 16 81

Given fractions are 8 9 , 10 27 , 16 81 HCF ( 8 9 , 10 27 , 16 81 ) = H C F o f t h e n u m e r a t o r s L C M o f t h e d e n o min a t o r s = H C F ( 8 , 10 , 16 ) L C M ( 9 , 27 , 81 ) Performing prime factorisation 8 = 2 3 10 = 2 × 5 16 = 2 4 So, the HCF ( 8 , 10 , 16 ) = 2 and LCM ( 9 , 27 , 81 ) = 3 4 = 81 Thus, HCF 8 9 , 10 27 , 16 81 = 2 81 And, LCM 8 9 , 10 27 , 16 81 = L C M o f n u m e r a t o r s H C F o f d e n o m i n a t o r s = L C M 8 , 10 , 16 H C F 9 , 27 , 81 Performing prime factorisation we get, 9 = 3 2 27 = 3 3 81 = 3 4 So, the HCF ( 9 , 27 , 81 ) = 3 2 = 9 and LCM ( 8 , 10 , 16 ) = 80 Thus, L C M 8 9 , 10 27 , 16 81 = 80 9 ⇒ H C F ( 8 9 , 10 27 , 16 81 ) = 2 81 and L C M ( 8 9 , 10 27 , 16 81 ) = 80 9

E M B I B E

Secondary School Mathematics for Class 10>Number Systems>Chapter 1 - Real Numbers>TEST YOURSELF

R S Aggarwal and Veena Aggarwal Solutions for Exercise 8: TEST YOURSELF

Author:R S Aggarwal & Veena Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal and Veena Aggarwal Solutions for Exercise 8: TEST YOURSELF

Attempt the free practice questions from Exercise 8: TEST YOURSELF with hints and solutions to strengthen your understanding. Secondary School Mathematics for Class 10 solutions are prepared by Experienced Embibe Experts.