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CBSE Class 10 Sample Paper for 2019 Boards

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Question 7 (Or 2nd) - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at March 23, 2023 by

Question 7 (OR 2 nd   question)

Show that 7 − √5 is irrational, give that √5 is irrational.

Show that 7 − √5 is irrational, give that √5 is irrational - Teachoo

Question 7 (Or 2nd) - CBSE Class 10 Sample Paper for 2019 Boards - Part 2

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Question 7 (OR 2nd question) Show that 7 − √5 is irrational, give that √5 is irrational. We have to prove 7 − √5 is irrational Let us assume the opposite, i.e., 7 − √5 is rational Hence, 7 − √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, 7 − √5 = 𝑎/𝑏 7 – 𝑎/𝑏 = √5 √5 = 7 – 𝑎/𝑏 √5 = (7𝑏 − 𝑎)/𝑏 Here, (7𝑏 − 𝑎)/𝑏 is a rational number But √5 is irrational Since, Rational ≠ Irrational This is a contradiction ∴ Our assumption is incorrect Hence, 7 − √5 is irrational Hence proved.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.