Question

उदाहरण 16 : दर्शाइए कि 5-√3 एक अपरिमेय संख्या है।
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Answer 1

Answer:

5-√3 is an irrational number.

Step-by-step explanation:

To prove 5-√3 is an irrational number.

We have to prove 5-√3 is not a rational number . ( Indirect proof)

Let's assume,

that,

5-√3 is a rational number which can be written as p/q. ...... 1

p/q is any rational number. ...... 2

Thus,

p/q = 5-√3 ..... from 1&2

p/5 = -√3×q

p/5 = -√3q

We know , that , √3 is an irrational number.

Thus, -√3q is also an irrational number.

Where as, p/5 is a rational number .

rational number = irrational number

i.e. p/5= -√3q is not possible

We arrive at a contradiction.

Therefore, 5-√3 is not a rational number.

Thus, 5-√3 is an irrational number