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why root 5 is irrational ?
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why root 5 is irrational ? Related: Important Definitions & Formulas:...
Let us demonstrate that √5 is an irrational number by proving the theorem.
Using the method of contradiction, it is possible to demonstrate the answer to this question. Let’s take it for granted that the number √5 is a rational number. If √5 is rational, then it may be expressed as an equation of the type a/b, here integers are a and b.
√5/1 = a/b
√5b = a
Bringing both sides into balance,
5b2 = a2
b2 = a2/5 —- (1)
This indicates that a2 is divided by 5.
That indicates that it can also divide a.
a/5 = c
a = 5c
On squaring, we get
a2 = 25c2
Replace a2 in the equation with its value (1).
5b2 = 25c2
b2 = 5c2
b2/5 = c2
This indicates that b2 may be divided by 5, and hence, b can likewise be divided by 5. Since this is the case, a and b share the factor 5 in common. However, this goes against the fact that a and b are in the coprime position. The fact that we made the assumption that √5 is a rational number led to the formation of this contradiction. As a result, we are forced to the conclusion that √5 is irrational.
Therefore √5 is an irrational number.
Courtesy ; Unacademy
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why root 5 is irrational ? Related: Important Definitions & Formulas: Real Numbers? 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 why root 5 is irrational ? Related: Important Definitions & Formulas: Real Numbers? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for why root 5 is irrational ? Related: Important Definitions & Formulas: Real Numbers?.
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