Prove root 7 is irrational

1.	Prove root 7 is irrational
Answer» Let root 7 be a rational numberThen,=√7 = a/b Now by squaring both side= (√7)² = (a/b)²= 7 = a²/b²= 7b² = a². (A²= 7b² from above)Here 7 divides a²Therefore 7 also divides aNow let a= 7c where c is some integerBy squaring both sides= A² = 49c²= 7b² = 49c²= B² = 7c²Here 7 divides b²Therefore 7 also divides bHere a and b both have common factor 7So our contradiction was wrong ,Therefore √7 is irrational First assume it that it is a rational number then your contradiction will be wrong and then you will prove it that it is irrrational and you can see in your book

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