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Sometimes it is and sometimes it isn't. The square root of 2 and the square root of 3 are both irrational, as is their product, the square root of 6. The square root of 2 and the square root of 8 are both irrational, but their product, the square root of 16, is rational (in fact, it equals 4).
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Example of two irrational numbers the product of which is an irrational number?
sqrt(2)*sqrt(3) is an irrational product.
What happens when two irrational numbers are multiplied?
You get a product which can be rational or irrational.
What product is true about the irrational and rational numbers?
The product of 2 rationals must be rational. The product of a rational and an irrational is irrational (unless the rational is 0) The product of two irrationals can be either rational or irrational.
Is 10x 3.14 irrational?
The product of two rational numbers, as in this example, is always RATIONAL.However, if you mean 10 x pi, pi is irrational; the product of a rational and an irrational number is ALWAYS IRRATIONAL, except for the special case in which the rational number is zero.
Is the product of any two irrational numbers is an irrational?
No. The product of sqrt(2) and sqrt(2) is 2, a rational number. Consider surds of the form a+sqrt(b) where a and b are rational but sqrt(b) is irrational. The surd has a conjugate pair which is a - sqrt(b). Both these are irrational, but their product is a2 - b, which is rational.
Example of two irrational numbers the product of which is an irrational number?
sqrt(2)*sqrt(3) is an irrational product.
What happens when two irrational numbers are multiplied?
You get a product which can be rational or irrational.
Why is the product of two rational number irrational?
The question is nonsense because the product of two rational numbers is never irrational.
What product is true about the irrational and rational numbers?
The product of 2 rationals must be rational. The product of a rational and an irrational is irrational (unless the rational is 0) The product of two irrationals can be either rational or irrational.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
What are two irrational numbers whose product is rational?
Make the two irrational numbers reciprocals of each other. Ex.) 1/pi x pi = 1
Give an example of two irrational numbers whose product is not irrational?
(pi) x (1/pi) = 1
Is the product of three irrational numbers always an irrational number?
No. The easiest counter-example to show that the product of two irrational numbers can be a rational number is that the product of √2 and √2 is 2. Likewise, the cube root of 2 is also an irrational number, but the product of 3√2, 3√2 and 3√2 is 2.
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.
If you add two irrational numbers do you get an irrational number?
Not necessarily. The sum of two irrational numbers can be rational or irrational.
Is the product of two irrational numbers is an integer?
It can be, but need not be. [sqrt(5)+sqrt(2)] and [sqrt(5)-sqrt(2)] are both irrational. Their product is 5-2 = 3. The two numbers are conjugates of one another and the property that their product is an integer is used to rationalise denominator of surds.
Write 3.0 as the product of two irrational numbers?
( pi ) x ( 3/pi ) = 3
