Prove that √5+√3 is irrational
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let √5+√3 be a rational number.
so √5+√3 =p/ q
squaring both sides we get
5+3+2√15 = p^2/q^2
= 2√15 = p^2 - 5q^2/q^2
= √15 = p^2 - 5q^2/2q^2
as we know that √15 is an irrational number.
so our supposition is wrong.
hence, √5 + √3 is an irrational number.
so √5+√3 =p/ q
squaring both sides we get
5+3+2√15 = p^2/q^2
= 2√15 = p^2 - 5q^2/q^2
= √15 = p^2 - 5q^2/2q^2
as we know that √15 is an irrational number.
so our supposition is wrong.
hence, √5 + √3 is an irrational number.
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