Question

Show that 5 -2√7is an irrational number

Answer 1

Answer:

If possible,let (5-2√7 ) be a rational number.Then,

(5-2√7 ) is rational and 5 is rational

{(5-2√7)-5} is rational

Since, differences of two rational is rational.

-2√7 is rational

(-1/2) (-2/7) is rational

Since, product of two rational is rational.

√7 is rational

This contradicts the face that √7 is irrational.

This contradiction arrises by assuming (5-2√7 ) as rational.

Hence,it is irrational.

Step-by-step explanation:

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