Question

Prove that 8- root 3 is irrational

Answer 1

Step-by-step explanation:

Let 8 - √3 be a rational number ( say r)

∴ 8 - √3 = r

⇒-√3 = r - 8

⇒√3 = 8 - r --1

According to equation 1, √3 is a rational number( ∵ r is rational)

This contradicts the fact that √3 is irrational

Therefore, our assumption is wrong

Hence 8 - √3 is an irrational number

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Answer 2

Answer:

Let 8 - √3 be a rational number ( say r)

∴ 8 - √3 = r

⇒-√3 = r - 8

⇒√3 = 8 - r --1

According to equation 1, √3 is a rational number( ∵ r is rational)

This contradicts the fact that √3 is irrational

Therefore, our assumption is wrong

Hence 8 - √3 is an irrational number

Step-by-step explanation: