Question

prove that 5+2√7 is irrational.given that√7is irrational​

Answer 1

Step-by-step explanation:

Let √7 =a/b, where a and b are coprime integer b is not equal to 0

Squaring both sides

Multiplying with b on both sides, we get

7b=a square /b

LHS=7 x b =Integers

RHS=a square /b = Integers/Integers=Rational Number

LHS is not equal to RHS

Our supposition is wrong

√7 is irrational

Let 5+2√7is a rational number

5+2√7=a/b where a and b are co prime b is not equal to 0

2√7=a/b - 5

√7=a-5b/2b

a-5b/2b is a rational

But √7 is irrational

√7 is not equal to a-5b/2b

Our supposition is wrong

5+2√7 is irrational

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