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Geometric mean

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Q: The square root of the product of two numbers is the of the number?
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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.).


All positive numbers have two square root a positive and a negative why?

The product of two negative numbers is a positive number. Ergo, the product of the square of a number is equal to the square of its negative equivalent.


Is the product of two irrational numbers always an irrational number?

No. The square root of two is an irrational number. If you multiply the square root of two by the square root of two, you get two which is a rational number.


Can the product of 2 irrational numbers be a rational number?

Yes. For example, the square root of 2 times the square root of 2 is equal to 2.


What are the squared numbers?

1,4,9,16,25,36,49,64,81,100,121,144! A square number is the answer to a number multiplied by itself. eg. 2x2=4 therefore 4 is the square number the square root, therefore, has to be two!


What is the geometric mean of 4 and 18?

Remember that the geometric mean is the he nth root of the product of n numbers. Since you have two numbers it will be the square root of their product. In this case that is square root of ( 4x18)=square root of (72) which is about 8.485


What is a whole number that can be named as a product of a number with itself called?

If it is product of an integer with itself, it is called a perfect square. Otherwise it has no name because all numbers are the product of some number with itself - viz the square root.


What is the number that is multiplied by another number to find the product?

"square root" if the two numbers are the same "multiplier" for any case


What are the rules for squares and squares roots?

With square roots if you have a number times itself or squared then that that product is that numbers square root example: 9x9= 81 81 square root is 9


Are 36 and 49 both Square numbers?

Yes, a square number means that it is the product of a number times the same number, so if you can divide a number buy the same number you get the square root. 6x6=36 and the square root of 36 is 6. 7x7 is 49 and the square root of 49 is 7. Make sense?


What two numbers has the sum of 52 and a product of 152?

The numbers are: 26 -square root of 524 and 26 +square root of 524


What kind of number has a square root?

A number that has a square root has to be able to be the product of two of the same numbers. Example: 4 x 4 = 16 16 can have a square root because 4 and 4 are the same. 10 can't have a square root because 2 x 5 = 10, and 2 and 5 aren't the same numbers.