Question 26 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Basic - Solutions of Sample Papers for Class 10 Boards

Last updated at July 27, 2026 by Teachoo

[SQP Class 10] Show that √2−√5 is an irrational number - Maths Basic - CBSE Class 10 Sample Paper for 2026 Boards - Maths Basic

part 2 - Question 26 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Basic - Solutions of Sample Papers for Class 10 Boards - Class 10

part 3 - Question 26 - CBSE Class 10 Sample Paper for 2026 Boards - Maths Basic - Solutions of Sample Papers for Class 10 Boards - Class 10

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Transcript

Question 26 Show that √2−√5 is an irrational number. We have to prove √2 − √5 is irrational Let us assume the opposite, i.e., √𝟐 − √𝟓 is rational Hence, √2 − √5 can be written in the form 𝑎/𝑏 where a and b (b≠ 0) are co-prime (no common factor other than 1) Hence, √𝟐 − √𝟓 = 𝒂/𝒃 Squaring both sides (√𝟐−√𝟓)^𝟐 =𝒂^𝟐/𝒃^𝟐 (√2)^2+(√5)^2−2 ×√2 ×√5=𝑎^2/𝑏^2 2+5−2 × √(2 × 5)=𝑎^2/𝑏^2 𝟕−𝟐 × √𝟏𝟎=𝒂^𝟐/𝒃^𝟐 −2 × √10=𝑎^2/𝑏^2 −7 √10=1/(−2) (𝑎^2/𝑏^2 −7) √𝟏𝟎=(−𝟏)/𝟐 (𝒂^𝟐/𝒃^𝟐 −𝟕) Here, (−1)/2 (𝑎^2/𝑏^2 −7) is a rational number But √10 is irrational Since, Rational ≠ Irrational This is a contradiction ∴ Our assumption is incorrect Therefore, √2−√5 is irrational Hence proved.

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