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Lets investigate.
To find an LCM you do a prime factorization and choose the factors, which are not in common raised to an appropriate power to show how many times it occurs in one of the 2 numbers AND use all factors that they do not have in common also to an approp. power.
Ex 1 LCM of 49 and 25
prime factorization yields 5x5 and 7x7
SO LCM will be (5x5)x(7x7) because they have no common factors
which equals 352
Ex 2 LCM of 100 and 36
prime factorization yields 5x5x2x2 and 3x3x2x2
They have common factors of 2x2 so use these but dont repeat them
So LCM = (5x5)x(3x3)x(2x2) = (5x3x2)x(5x3x2) = 302
So every square (A) when factored becomes either (a x a) or (b x b x c x c) etc.
Lets find the LCM of A and N where A and N are squares, but not equal.
Prime factorization A = ( a x a x b x b) and N = ( n x n x p x p x a x a)
LCM will equal (b x b) x ( n x n x p x p) x (a x a) <-- common factors
= (a x b x n x p) x (a x b x n x p)
= (a x b x n x p)2 which is a square.
The rules for forming a LCM force you to make a square because each original number has a prime factorization that has 2 factors, and you must use both or you will not form a LCM.
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Are square numbers always even?
No, but only in the case of the number 1 (12=1) are square numbers odd.
True or false the LCM of two square numbers is another square number?
True.
Are square numbers are always odd?
No. The square of an odd number will be odd and the square of an even number will be even.Examples:5x5=2511x11=12115x15=2254x4=168x8=6416x16=256
Is the square root of any composite numbers irrational?
The square root of a composite number is not always an irrational number. e.g. 4 is a composite number and its square root is 41/2 = 2, which is rational number.
What three square numbers that add to another square number?
There are infinitely many possible answers. The smallest set of numbers is (9, 16, 144, 169)
Is the LCM of 2 square numbers always another square number?
Yes
What is the product of a counting number and itself?
That's the "square" of the number. With counting numbers, the square will always be another counting number.
When a square number is subtracted by another square number answer 9 what is the square numbers?
htgubnm9mjh
Does a square number multiplied by another always equal a square number?
=== === No === ===
When you subtract one square number from another square number the answer is 16 what was the first number?
when you subtract one square number with another the answer is 16 what are the two numbers
When you subtract a square number from another square number you get 5 what are the two square numbers?
4 and 9
When you subtract one square number another square number the answer is 12 what re the two asquare numbers?
The square numbers are: 16-4 = 12
Would the least common multiple of two squared numbers be another square number?
Another square number.
Is a square of a number always bigger than the number?
all of the numbers, except the numbers 1 and below
Are square numbers always even?
No, but only in the case of the number 1 (12=1) are square numbers odd.
Does there exist an irrational number such that its square root is rational?
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
What square numbers do you get when you subtract one square number from another number and the answer is 12?
16 and 4
