The square root of any composite number is an irrational number. Ture or False. Why?

Answer 1

False. 36 is composite, and √36=6, which is rational.

Answer 2

not always
for example 6 is a composite no and the square root of 6 is irrational as it is equal to rt2*rt3,both irrational
or take anothe composite no 12.its root is 2 rt 3 again irrational
whereas 64 is a composite no and its root is 8 which is ratioanl

Answer 3

Maybe you're looking for this:

The square root of any non-square integer is irrational.

Proof:
Let n be an integer and let the ireducible fraction p/q be the squareroot of n. We want to show that either q is 1. This will prove that n is a square number.

We have n = p^2/q^2. Since this is an integer, all prime factors in q^2 are also prime factors in p^2. But p^2 has the same prime factors as p and q^2 the same prime factors as q, so all prime factors in q are also prime factors in p. If q has no prime factors, it is 1, as we wanted to show. But if q has at least one prime factor, the fraction p/q can be reduced by that factor. But we assumed p/q to be ireducible so that's a contradiction. Q.e.d.

Answer 4

False
Since composite number is 4 whose sq rt is 2 which is not irrational

Answer 5

to have irrational square root, the number must not be a perfect square....whether composite or not....

if N is not a perfect square, then sqrt(N) is always an irrational number......

(it is also by definition... if the root terminates at a place, then N must be perfect...)

Answer 6

The square root of any square is rational. What is
true is the square root of any whole number that is
not a square is irrational.

Answer 7

not true

irational numbers are Pi, Pi/2 or a number that has no end with out repeating didits

like 3.44444444444444444444....and so is not irrational
but 3.9275683956792739102005...is irrational

Answer 8

It would be true if you had asked for non-square composites.