Question

Prove that 15+17√3 be an irrational number

Answer 1

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Let 15 + 17√3 is a rational number.

p/q = 15 + 17√3 q is not equal to zero

p and q are integers.

p/q = 15 + 17√3

=> p - 15/q = 17√3

Rational number = Irrational number

This is contridication.

Hence , 15 + 17√3 is an irrational number.







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Answer 2

Answer:

symbol which I used

^ = root

Step-by-step explanation:

Let us assume to the contrary that 15 +17^3 is a rational number

15+17^3 = a/b , where a and b are co-primes , b is not equal to zero

15+17^3 = a/b

17^3 = a/b-15 (shift 15 left side +15 becomes -15)

^3 = a-15b/17b (shift 17 to denominator )

a-15b/17b = rational number

but ^3 is irrational

The contradiction arisen due to our wrong assumption that 15+17^3 is ration number

Hence 15+17^3 is an irrational number

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