Question

prove that root 3+root 5is an irrational number​

Answer 1

Let √3+√5 be any rational number x

x=√3+√5

squaring both sides

x²=(√3+√5)²

x²=3+5+2√15

x²=8+2√15

x²-8=2√15

(x²-8)/2=√15

as x is a rational number so x²is also a rational number, 8 and 2 are rational nos.

so √15 must also be a rational number as quotient of two rational numbers is rational

but, √15 is an irrational number.

this shows that our Contradiction was wrong.

so √3+√5 is not a rational number.

LONG LIVE THE FILTER BOY

Answer 2

Answer:

ok i will explain but u follow me then ok

Step-by-step explanation:

Let as assume on contrary that 

√3 + √5 

is a rational number. 

Then there exists co - prime integers p and q such that  

root 3+root5 =p/q

p/q-root3=root5

p/q-root3 is an rational no. so,roots 5 ia also a rational no. but this contradicts our assumption is wrong we know that root 5 is an irrational no. so that on our contradicts

root3+root5is an irrational no.