Question

prove that root 5 +3 is an irratinal number

please answer this ​

Answer 1

ANSWER:

• √5+3 is an Irrational number.

GIVEN:

• Number = √5+3

TO PROVE:

• √5+3 is an Irrational number.

SOLUTION:

Let √5+3 be a rational number which can be expressed in the form of p/q where p and q have no other common factor than 1.

$\implies \: \sqrt{5} + 3 = \dfrac{p}{q} \\ \\ \implies \: \sqrt{5} = \dfrac{p}{q} - 3 \\ \\ \implies \: \sqrt{5} = \dfrac{p - 3q}{q}$

Here:

• (p-3q)/q is rational but √5 is an Irrational number.
• Thus our contradiction is wrong.
• √5+3 is an Irrational number.