Prove root 3 + root 5 is irrational?

1.	Prove root 3 + root 5 is irrational?
Answer» ong>Answer: yes Step-by-step explanation: LET V3+v5 be a rational number. A rational number can be written in the form of p/q where p,q are INTEGERS. V3+v5 = p/q V3 = p/q-v5 Squaring on both sides, (V3)? = (p/q-15) 3 = p/q²+v5?-2(p/q)(v5) %D V5x2p/q = p?/q?+5-3 v5 = (p?+2q?)/q² × q/2p V5 = (p?+2q?)/2pq p,q are integers then (p2+2q/2pq is a Then v5 is also a rational number. rational number. But this contradicts the fact that v5 is an IRRATIONAL number. So,our supposition is false. Therefore, v3+v5 is an irrational number.

Answer»

ong>Answer:

yes

Step-by-step explanation:

LET V3+v5 be a rational number. A rational number can be written in the form of p/q where p,q are INTEGERS.

V3+v5 = p/q V3 = p/q-v5

Squaring on both sides,

(V3)? = (p/q-15)

3 = p/q²+v5?-2(p/q)(v5) %D

V5x2p/q = p?/q?+5-3 v5 = (p?+2q?)/q² × q/2p

V5 = (p?+2q?)/2pq

p,q are integers then (p2+2q/2pq is a Then v5 is also a rational number.

rational number.

But this contradicts the fact that v5 is an

IRRATIONAL number.

So,our supposition is false.

Therefore, v3+v5 is an irrational number.

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