Question

Root 3+ root 5 the whole square- prove it is irrational

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Solution:-

Let ( √3 + √5)² be Rational Number.

=) ( √3 + √5)² can be written in the form of p/q , where p and Q are some integers and Q is not equal to 0.

=) (√3 + √5)² = p/q

=) 3 + 5 + 2√15 = p/q

=) 2√15 = p/q - 8

=) √15 = (p/q -8)/2

Suppose,

(p/q -8)/2 is an Rational Number.

But √15 is an Irrational Number.

Thus, It Contradicts our supposition that ( √3 + √5)² is a Rational Number.

Hence,

( √3 + √5)² is a Rational Number.