Question

Prove that 15 + 17 root3 is an irrational number

Answer 1

Step-by-step explanation:

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Suppose 15+173–√ is a rational number.

∴15+173–√=ab, where a and b are co-prime, b≠0

⇒173–√=ab−15

3–√=a−15b17b

a−15b17b is rational number,

3–√ is irrational.

∴3–√≠a−15b17b

∴ Our supposition is wrong.

⇒15+173–√ is irrational.

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