Question

prove that root 3 + root 5 is an irrational number



I all be thankful to whoever's will answer it​

Answer 1

Answer:

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

so we arrive at a contradiction t

this shows that our supposition was wrong

so √3+√5 is not a rational number

or

we know that, √3 and √5 are irrational numbers

so we know that sum of two irrational numbers is also irrational

√3+√5 is also irrational.

hope this helps

Answer 2

Step-by-step explanation:

assume that √5+√3..is irrational number

so,√5+√3 is irrational (assume)so they must be in the form of p/q,where q not equal to zero

and p and q are integers

√5=2.2...

√3=1.71..

so our assuming is wrong √3+√5

is an irrational number

pls mark me as brainlist