# prove that 7√2/5 is irrational

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**Answer:**

**Step-by-step explanation:**

Let us assume 7-2√5 is rational.

Let 7-2√5 = a/b, where a, b are integers

and b ≠ 0 .

-2√5 = ( a/b ) - 7

=> -2√5 = ( a - 7b )/b

=> √5 = ( a - 7b )/( -2b )

=> √5 = ( 7b - a )/2b

Since , a,b are integers , (7b-a)/2a is

rational , and so √5 is rational.

This contradicts the fact that √5 is

irrational .

Hence , 7 - 2√5 is irrational.

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