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Is the sum of any two irrational number is an irrational number?
The sum of two irrational numbers may be rational, or irrational.
Does an irrational number multiplied by an irrational number equal an irrational number?
The product of two irrational numbers may be rational or irrational. For example, sqrt(2) is irrational, and sqrt(2)*sqrt(2) = 2, a rational number. On the other hand, (2^(1/4)) * (2^(1/4)) = 2^(1/2) = sqrt(2), so here two irrational numbers multiply to give an irrational number.
Which number produces an irrational number when multiplied by?
At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.
Identify of rational and irrational numbers?
A rational number is a number that can be expressed as a ratio of two integers in the form A/B where B>0. An irrational number is a real number that is not rational.
Can you add two irrational numbers to get a rational number?
Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.
Is the product of two rational number irrational or rational?
It is always rational.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
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.
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.).
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.
What two irrational numbers make a rational number?
The simplest example (of infinitely many) is probably the squareroot of two multiplied by itself equals two. Take any rational number, say 4.177 and divide it with any irrational number, say the square root of 13, and you will get a new irrational number. The product of your two irrational numbers now make a rational number.
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.
What happens when two irrational numbers are multiplied?
You get a product which can be rational or irrational.
What is the Next to rational and irrational number?
Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).
Is there any number x such that x² is an irrational number and x's is a rational number?
no x² is the product of 2 rational numbers in this case the same 2 numbers x and x The product of two rational numbers is always rational.
When the product of two irrational numbers equals a rational number then what are the factors called?
They are called conjugates.
