Question

Prove that 43 + Root5 is aan irrational number.​

Answer 1

Required Answer:-

Question:

• Prove that 43 + √5 is irrational.

Proof:

Let us assume that 43 + √5 is a rational number, say r.

Therefore,

➡ 43 + √5 = r

➡ √5 = r - 43

As r is rational,

➡ r - 43 is rational.

➡ √5 is irational.

But this contradicts the fact that √5 is irrational.

★ Hence, our assumption is wrong. Therefore, 43 + √5 is an irrational number.

Learn More:

• Rational Number: A number that can be represented in p/q form where q ≠ 0 and p, q have no common factors (except 1) is called a rational number. Example - 2, 3, 2/3, 2.5 etc.
• Irrational Number: A number that cannot be represented in p/q form where q ≠ 0 and p, q have no common factors (except 1) is called an irrational number. Example: √2, √3 etc. Square root of any prime number is irrational.