Question

prove that 2- 2root 5 is irrational number ​

Answer 1

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PLZZ MARK BRAINLIEST

Answer 2

Let, 2-2√5 be a rational number.

We know 2 and 1/2 are rational numbers.

Also,

Rational - Rational = Rational

=> 2-(2-2√5) = Rational

=> 2 - 2 + 2√5 = Rational

=> 2√5 = Rational

Also,

Rational x Rational = Rational

=> 2√5 x 1/2 = Rational

=> √5 = Rational

But √5 is an irrational number. Hence, contradiction of our supposition.

Thus, 2-2√5 is an irrational number.