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Home » Prove that (2 √3 – 1) is irrational.
Prove that (2 √3 – 1) is irrational.
CBSE | Class 10 | Exercise 1D | Maths | Real Numbers | RS Aggarwal
Prove that (2 √3 – 1) is irrational.

Answer:

Consider,

x = 2 √3 – 1 be a rational number.

x = 2 √3 – 1

x2 = (2 √3 – 1)2

x2 = (2 √3 )2 + (1)2 – 2(2 √3)(1)

x2 = 12 + 1 – 4 √3

x2 – 13 = – 4 √3

\frac{13-{{x}^{2}}}{4}=>\sqrt{3}

x – rational number, x2 – rational number

13 – x

2 – rational number

\frac{13-{{x}^{2}}}{4} is a rational number

√3 is a rational number

But √3 is an irrational number, which is a contradiction.

The assumption is wrong.

Hence, (2 √3 – 1) is an irrational number.

 

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