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Show that 5 - 3√2 is irrational.
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Show that 5 - 3√2 is irrational. Related: Ex 1.3 NCERT Solutions, Rea...
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Show that 5 - 3√2 is irrational. Related: Ex 1.3 NCERT Solutions, Rea...
Proof that 5 - 3√2 is irrational:
Assumption: Let's assume that 5 - 3√2 is rational.
Definition: A rational number is a number that can be expressed in the form p/q, where p and q are integers and q is not equal to 0.
Representation: So, we can represent 5 - 3√2 as p/q, where p and q are integers and q is not equal to 0.
Algebraic Manipulation: Multiplying the numerator and denominator by the conjugate of 5 - 3√2, which is 5 + 3√2, we get:
(5 - 3√2) * (5 + 3√2) / (5 + 3√2)
= (25 - 9*2) / (5 + 3√2)
= (7) / (5 + 3√2)
Contradiction: Now we have a contradiction, as we have expressed 5 - 3√2 as a rational number (7 / (5 + 3√2)), which violates our assumption. Hence, our assumption is wrong.
Conclusion: Therefore, 5 - 3√2 is irrational.
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Show that 5 - 3√2 is irrational. Related: Ex 1.3 NCERT Solutions, Real Numbers - Mathematics for Class 10th
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Show that 5 - 3√2 is irrational. Related: Ex 1.3 NCERT Solutions, Real Numbers - Mathematics for Class 10th for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Show that 5 - 3√2 is irrational. Related: Ex 1.3 NCERT Solutions, Real Numbers - Mathematics for Class 10th covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that 5 - 3√2 is irrational. Related: Ex 1.3 NCERT Solutions, Real Numbers - Mathematics for Class 10th.
Show that 5 - 3√2 is irrational. Related: Ex 1.3 NCERT Solutions, Real Numbers - Mathematics for Class 10th for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Show that 5 - 3√2 is irrational. Related: Ex 1.3 NCERT Solutions, Real Numbers - Mathematics for Class 10th covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that 5 - 3√2 is irrational. Related: Ex 1.3 NCERT Solutions, Real Numbers - Mathematics for Class 10th.
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