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prove that root 2 + root 3 + root 5 is irrational
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prove that root 2 + root 3 + root 5 is irrational
Proof that √2 √3 √5 is irrational:
Assumption: Let us assume that √2 √3 √5 is rational.
Definition of a rational number: A rational number is a number that can be expressed as a fraction of two integers.
Expressing √2 √3 √5 as a fraction: Since √2 √3 √5 is a rational number, it can be expressed as a fraction of two integers. Let us express it as p/q, where p and q are integers and q is not equal to zero.
Simplifying the expression: We can simplify the expression as follows:
√2 √3 √5 = √2 * √3 * √5
= √(2 * 3 * 5)
= √30
∴ p/q = √30
Squaring both sides: Squaring both sides of the equation, we get:
(p/q)^2 = (√30)^2
p^2/q^2 = 30
Conclusion: Since 30 is not a perfect square, it cannot be expressed as a fraction of two integers. Hence, our assumption that √2 √3 √5 is rational is incorrect.
Therefore, √2 √3 √5 is irrational.
Assumption: Let us assume that √2 √3 √5 is rational.
Definition of a rational number: A rational number is a number that can be expressed as a fraction of two integers.
Expressing √2 √3 √5 as a fraction: Since √2 √3 √5 is a rational number, it can be expressed as a fraction of two integers. Let us express it as p/q, where p and q are integers and q is not equal to zero.
Simplifying the expression: We can simplify the expression as follows:
√2 √3 √5 = √2 * √3 * √5
= √(2 * 3 * 5)
= √30
∴ p/q = √30
Squaring both sides: Squaring both sides of the equation, we get:
(p/q)^2 = (√30)^2
p^2/q^2 = 30
Conclusion: Since 30 is not a perfect square, it cannot be expressed as a fraction of two integers. Hence, our assumption that √2 √3 √5 is rational is incorrect.
Therefore, √2 √3 √5 is irrational.
Community Answer
prove that root 2 + root 3 + root 5 is irrational
it's irrational because sum of irrational numbers is irrational.....
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prove that root 2 + root 3 + root 5 is irrational
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prove that root 2 + root 3 + root 5 is irrational 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 prove that root 2 + root 3 + root 5 is irrational covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for prove that root 2 + root 3 + root 5 is irrational .
prove that root 2 + root 3 + root 5 is irrational 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 prove that root 2 + root 3 + root 5 is irrational covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for prove that root 2 + root 3 + root 5 is irrational .
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