CBSE Class 10 Sample Paper for 2026 Boards - Maths Basic
You are here
CBSE Class 10 Sample Paper for 2026 Boards - Maths Basic
Last updated at Sept. 10, 2025 by Teachoo
Get access to this page and all premium solutions, videos, and worksheets by joining Teachoo Black.
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.
