Question

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Show that root
$( \sqrt{3} + \sqrt{5} ) ^{2}$
is an irrational number ​

Answer 1

Answer:

$= > 3 + 5 + 2 \sqrt{15} \\ = > 8 + 2 \sqrt{15}$

Answer 2

Answer:

(√3+√5)²=(8+2√15)

Step-by-step explanation:

If possible, let (8+2√15) be rational;

Thus, (8+2√15) can be represented in the form of p/q; where p and q are coprime integers, q≠0.

i.e., 8+2√15=p/q

2√15=(p-8q)/p

√15 = (p-8q)/2p

this means that √15 is rational, as it is represented in the form of p/q.

But, this contradicts the fact that √15 is irrational.

This contradiction arises because of our wrong assumption that (√3+√5)² is rational.

Therefore, (√3+√5)² is irrational.

Hence, proved