Example 12 - Check whether 7 root 5, ... are irrational - Examples

  1. Chapter 1 Class 9 Number Systems
  2. Serial order wise
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Example 12(Method 1) Check whether 7 √5, 7/√5, √2 + 21, πœ‹ – 2 are irrational numbers or not. 7 βˆšπŸ“ 7 is rational √5 = 2.236…. which is non- terminating non-repeating is an irrational number We know that Rational Γ— Irrational = Irrational Since, 7 √5 = 7 Γ— √5 it is irrational πŸ•/βˆšπŸ“ 7 is rational √5 = 2.236…. which is non- terminating non-repeating is an irrational number We know that π‘…π‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™/πΌπ‘Ÿπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™ = Irrational Thus, 7/√5 is irrational √𝟐 + 21 21 is rational √2 " = 1.4142…" which is non- terminating non-repeating is an irrational number We know that Irrational + Rational = Irrational Thus, √2 + 21 is an irrational number 𝝅 – 2 2 is rational πœ‹ = 3.1415…. which is non- terminating non-repeating is an irrational number We know that Irrational – Rational = Irrational Thus, πœ‹ - 2 is an irrational number Example 12 (Method 2) Check whether 7 √5, 7/√5, √2 + 21, πœ‹ – 2 are irrational numbers or not. 7 βˆšπŸ“ √5 = 2.236…. 7 √5 = 7 Γ— (2.346) = 15.652….., It is a non-terminating and non-repeating decimal expansion. So,7 √5 is an irrational number πŸ•/βˆšπŸ“ 7/√5 = (7√5)/(√5 √5) = (7√5)/5 = 7/5 Γ— (2.346) = 3.1304…. It is a non-terminating and non-repeating decimal expansion. So, 7/√5 is an irrational number √𝟐 + 21 √2 = 1.4142… √2 + 21 = 1.4142 + 21 = 22.4142……, It is a non-terminating and non-repeating decimal expansion. So, √2 + 21 is an irrational number 𝝅 – 2 πœ‹ = 3.1415…. πœ‹ – 2 = 3.1415…. – 2 = 1.1415…… It is a non-terminating and non-repeating decimal expansion. So, πœ‹ - 2 is an irrational number

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.