Question

Prove root 8 is irrational

Answer 1

Answer:

√8 is irrational.

Step-by-step explanation:

Let us assume √8 be rational so that it can be written in the form of a/b where a and b co-primes. then,

√8=a/b

b√8=a

Now, by squaring both sides, we get that:

8 = a²/b²

and 8b² = a²

this implies 8 divides a² which also means 8 divides a.

so there exists a p within the integers such that:

a = 8p

and thus,

√8 = 8p/b

which implies

8 = 64p²/b²

which is:

1/8 = p²/b²

or:

b²/p² = 8

which implies

b² = 8p²

which implies 8 divides b² which means 8 divides b.

8 divides a, and 8 divides b, which is a contradiction because common factor of (a, b) = 1

Therefore, √8 is irrational.

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i hope it will helps you friend

Answer 2

Answer:

Answer:

√8 is irrational.

Step-by-step explanation:

Let us assume √8 be rational so that it can be written in the form of a/b where a and b co-primes. then,

√8=a/b

b√8=a

Now, by squaring both sides, we get that:

8 = a²/b²

and 8b² = a²

this implies 8 divides a² which also means 8 divides a.

so there exists a p within the integers such that:

a = 8p

and thus,

√8 = 8p/b

which implies

8 = 64p²/b²

which is:

1/8 = p²/b²

or:

b²/p² = 8

which implies

b² = 8p²

which implies 8 divides b² which means 8 divides b.

8 divides a, and 8 divides b, which is a contradiction because common factor of (a, b) = 1

Therefore, √8 is irrational.

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i hope it will helps you friend

Step-by-step explanation: