Question

prove that 6+√13 is irrational​

Answer 1

Required Answer:-

Question:

• Prove that 6 + √13 is irrational.

Proof:

Let us assume that 6 + √13 is rational, say r.

Then,

➡ 6 + √13 = r

➡ √13 = r - 6

As r is rational,

➡ r - 6 is rational.

➡ √13 is rational.

But this contradicts the fact that √13 is irrational.

Hence, our assumption is wrong.

Therefore,

➡ 6 + √13 is an irrational number. (Hence Proved)

Learn More:

• Rational Number: A number that can be expressed in p/q form where q ≠ 0 and p, q have no common factors (except 1) is called rational number. Example: 1,2,2/3,4/9 etc.
• Irrational Number: A number that cannot be expressed in p/q form where q ≠ 0 and p, q have no common factors (except 1) is called irrational number. Example: √2, √3, √5, π, etc.

Answer 2

Answer:

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