Question

prove that √3-√5 is an irrational​

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 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

hope this helps