Question

prove that √3+√5 is a 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

so we arrive at a contradiction t

this shows that our supposition was wrong

so √3+√5 is not a rational number

Answer 2

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..

$OR \: U \: CAN \: DO \: IT \: LIKE \: THIS \: : \:$

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..