prove that root3 +root5 is an irrational number
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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
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
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