Suppose the square root of 88 is rational. That is, it is of the form p/q where p and q are integers (q ≠0) and where p and q have no common factors so that the fraction is in its simplest form.
Then (p/q)2 = 88
p2/q2 = 88
or p2 = 88*q2
Now 11 divides the right hand side so 11 must divide the left hand side. That is 11 divides p2 and since 11 is prime, 11 must divide p.
Therefore p = 11*r where r is some integer.
So now we have (11r)2 = 88*q2
or 121*r2 = 88*q2
which simplifies to 11*r2 = 8*q2
11 divides the left hand side and so must divide the right hand side and since 11 cannot divide 8, it must divide q2 and since 11 is a prime, it must divide q.
But that means that 11 is a common factor of p and q, contrary to p/q being in the simplest form. Therefore no such rational fraction can exist and so the square root of 88 is irrational.
Yes.
Yes.
irrational
It is a irrational number. Because the square root of every imperfect square is irrational number.
Yes, square root of 33 is irrational.
Irrational.
Yes.
Yes.
The square root of 94 is an irrational number
The square root of 200 is irrational.
irrational
Oh, dude, negative square roots are actually considered irrational numbers. I know, right? It's like, they're not rational because they can't be expressed as a simple fraction. So yeah, negative square roots are definitely in the irrational club. Cool, right?
It is a irrational number. Because the square root of every imperfect square is irrational number.
The square root of 12 is an irrational number
The square root of 12 is an irrational number
The square root of 0.144 is an irrational number
Yes, square root of 33 is irrational.