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Home » Prove that (4 – 5√2) is irrational.
Prove that (4 – 5√2) is irrational.
CBSE | Class 10 | Exercise 1D | Maths | Real Numbers | RS Aggarwal
Prove that (4 – 5√2) is irrational.

Answer:

Consider,

x = 4 – 5√2 be a rational number.

x = 4 – 5√2

x2 = (4 – 5√2)2

x2 = 42 + (5√2)2 – 2(4) (5√2)

x2 = 16 + 50 – 40√2

x2 – 66

x2 = – 40√2

=> \frac{66-{{x}^{2}}}{40}

=> √2

x is a rational number, x2  is also a rational number.

⇒ 66 – x

2 is a rational number

\frac{66-{{x}^{2}}}{40} is a rational number

√2 – rational number

But √2 is an irrational number, which is a contradiction.

The assumption is wrong.

Hence, (4 – 5√2) is an irrational number.

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