prove that 2√5+3 is irrational number
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Answer:
Given below
Step-by-step explanation:
Let 2 + 5√3 = a, where a is a rational number.
√3 = (a – 2)/5
Which is a contradiction as LHS is irrational and RHS is rational.
∴ 2 + 5√3 can not be rational.
Hence, 2 + 5√3 + is irrational.
Alternate Method
Let 2 + 5√3 be rational.
∴ 2 + 5√3 = p/q ; p, q are integers, q ≠ 0
⇒ √3 = (p/q - 2) ÷ 5
√3 = (p - 2q)/5q
LHS is irrational and RHS is rational which is a contradiction.
∴ 2 + 5√3 is irrational.
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