Ekercise lasBrowthat is is inationalemon, to the con ball

1.	Ekercise lasBrowthat is is inationalemon, to the con ball
Answer» Let us assume that √5 as rational number If a and b are two co prime number and b is not equal to 0.We can write √5 = a/b Multiply by b both side we getb√5 = a Squaring on both sides, we get5b² = a²..........(1) Therefore, 5 divides a² and according to theorem of rational number, for any prime number p which is divides a² then it will divide a also. That means 5 will divide a. So we can writea = 5cand put the value of a in equation (1) we get 5b² = (5c)²5b² = 25c² Divide by 25 we getb²/5 = c² Again using same theorem we get that b will divide by 5and we have already get that a is divide by 5but a and b are co prime number. This is contradiction to the fact that√5 is rationalThus √5 is irrational

Answer»

Let us assume that √5 as rational number

If a and b are two co prime number and b is not equal to 0.We can write √5 = a/b

Multiply by b both side we getb√5 = a

Squaring on both sides, we get5b² = a²..........(1)

Therefore, 5 divides a² and according to theorem of rational number, for any prime number p which is divides a² then it will divide a also.

That means 5 will divide a. So we can writea = 5cand put the value of a in equation (1) we get

5b² = (5c)²5b² = 25c²

Divide by 25 we getb²/5 = c²

Again using same theorem we get that b will divide by 5and we have already get that a is divide by 5but a and b are co prime number.

This is contradiction to the fact that√5 is rationalThus √5 is irrational

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