If x = 2 - 1 then write the value of 1 x .

Given that x = 2 - 1 . Hence 1 x is given as 1 x = 1 2 - 1 . We know that rationalization factor for 2 - 1 is 2 + 1 . We will multiply each side of the given expression 1 2 - 1 by 2 + 1 1 2 - 1 × 2 + 1 2 + 1 = 2 + 1 ( 2 ) 2 - ( 1 ) 2 ∵ a 2 - b 2 = ( a + b ) ( a - b ) = 2 + 1 2 - 1 = 2 + 1 . Hence, the value of the given expression is 2 + 1 .

Write the rationalization factor of 5 - 2

Given that 5 - 2 . To make the denominators free from square roots, we multiply the numerator and denominator by an irrational number. Such a number is called rationalization factor. We know that rationalization factor of a - b is a + b . So, the rationalization factor of 5 - 2 is 5 + 2 . Therefore, the required answer is 5 + 2 .

We are asked to simplify 3 + 2 2 . The given expression can be written in the form ( a + b ) 2 = a 2 + b 2 + 2 a b as 3 + 2 2 = 2 + 1 + 2 × 1 × 2 = ( 2 ) 2 + ( 1 ) 2 + 2 × 1 × 2 = ( 2 + 1 ) 2 = 2 + 1 . Hence, the value of given expression is 2 + 1 .

We are asked to simplify 3 - 2 2 . The given expression can be written in the form ( a - b ) 2 = a 2 + b 2 - 2 a b as 3 - 2 2 = 2 + 1 - 2 × 1 × 2 = ( 2 ) 2 + ( 1 ) 2 - 2 × 1 × 2 = ( 2 - 1 ) 2 = 2 - 1 . Hence, the value of the given expression is 2 - 1 .

E M B I B E

Mathematics Class 9>Chapter 3 - Rationalisation>VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)

R. D. Sharma Solutions for Chapter: Rationalisation, Exercise 3: VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)

Author:R. D. Sharma

R. D. Sharma Mathematics Solutions for Exercise - R. D. Sharma Solutions for Chapter: Rationalisation, Exercise 3: VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)

Attempt the practice questions on Chapter 3: Rationalisation, Exercise 3: VERY SHORT ANSWER TYPE QUESTIONS (VSAQs) with hints and solutions to strengthen your understanding. Mathematics Class 9 solutions are prepared by Experienced Embibe Experts.