CBSE Class 10 Sample Paper for 2027 Boards - Maths Standard

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Question 26 - CBSE Class 10 Sample Paper for 2027 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at October 9, 2026 by

Question 26 — slide 74

Question 26 — slide 75

Question 26 — slide 76

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Transcript

Question 26 Given that sqrt(3) is irrational number, prove that (2+3sqrt(3)) is an irrational number. We have to prove 2 + 3sqrt(3) is irrational Let us assume the opposite, i.e., 2 + 3sqrt(๐Ÿ‘) is rational Hence, 2 + 3sqrt(3) can be written in the form (๐‘Ž)/(๐‘) where a and b (bโ‰  0) are co-prime (no common factor other than 1) Hence, 2 + 3sqrt(๐Ÿ‘) = (๐’‚)/(๐’ƒ) 3sqrt(3) = (๐‘Ž)/(๐‘) โˆ’ 2 sqrt(3) = (๐‘Ž)/(3๐‘) โˆ’ (2)/(3) sqrt(๐Ÿ‘) = (๐’‚ โˆ’๐Ÿ๐’ƒ)/(๐Ÿ‘๐’ƒ) Here, (๐’‚ โˆ’๐Ÿ๐’ƒ)/(๐Ÿ‘๐’ƒ) is a rational number But sqrt(3) is irrational Since, Rational โ‰  Irrational This is a contradiction โˆด Our assumption is incorrect Irrational Rational Hence, 2 + 3sqrt(๐Ÿ‘) is irrational Hence proved.

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