Question

prove that root3 + 5 is not a rational no​

Answer 1

Answer:

Step-by-step explanation:

Let √3+5 is a rational no.

Where √3+5 =p/q ( where q is not equal to zero and p and q are integers )

√3=p/q - 5 ( by rearranging them )

Since p and q are integers but as we get p/q -5 which is rational and √3 is irrational so , it is a contradiction which arise due to our wrong .assumption

Answer 2

Let X be any rational number.....

So,x=√3+√5

Now,Squaring both sides ,

X²={√3 +√5}²

x²=3+5+2√15. {BY IDENTITY OF (a+b)²}

So x²-8=2√15

or x²-8 ÷2=√15

Here x²-8 divided by 2 is rational

but this contradict the fact that √15 is irrational

Hence,√3+√5 is irrationalll

Hope it help u !