Prove that √2 + √3 is an irrational number
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Prove that √2 + √3 is an irrational number
Guys Please Answer!!
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let ,√2 and √3 is a rational number
we find co- primes a and b (b is not equal to 0) such that
√2 + √3=a/b
squaring on both sides
(√2+√3) whole square =a/b whole square
2+3+2×√2√3=a square /b square
6+2√6= a square / b square
2√6= a square / b square-6
sins a and b are integers,a square by b square minus 6 is a rational number and 2 root 6 is a irrational number but this contradicts our assumption
hence√2+√3 is a irrational number