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The conjugate of an irrational number is a non-zero number such that the product of the two numbers is rational.
In high school mathematics, you are usually required to know only the conjugates of surds of the form a + b*sqrt(x).
The conjugate is a - b*sqrt(x)
[-a + b*sqrt(x) is also a conjugate - all you need to do is to switch the sign of one of the two terms.]
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What is the conjugate of square root of 13?
If the square root of a number is irrational, it is its own conjugate. sqrt(13)*sqrt(13) = 13 and you no longer have an irrational!
How do you rationalise the denominator?
It depends on what the denominator was to start with: a surd or irrational or a complex number. You need to find the conjugate and multiply the numerator by this conjugate as well as the denominator by the conjugate. Since multiplication is by [conjugate over conjugate], which equals 1, the value is not affected. If a and b are rational numbers, then conjugate of sqrt(b) = sqrt(b) conjugate of a + sqrt(b) = a - sqrt(b), and conjugate of a + ib = a - ib where i is the imaginary square root of -1.
The sum of two irrational is always irrational?
No. In fact, the sum of conjugate irrational numbers is always rational.For example, 2 + sqrt(3) and 2 - sqrt(3) are both irrational, but their sum is 4, which is rational.
Is an irrational number plus an irrational number rational?
No. The sum of an irrational number and any other [real] number is irrational.
What is a negative irrational number?
A negative irrational number can be thought of as an irrational number multiplied by -1, or an irrational number with a minus sign in front of it.
What is the conjugate of square root of 13?
If the square root of a number is irrational, it is its own conjugate. sqrt(13)*sqrt(13) = 13 and you no longer have an irrational!
How do you rationalise the denominator?
It depends on what the denominator was to start with: a surd or irrational or a complex number. You need to find the conjugate and multiply the numerator by this conjugate as well as the denominator by the conjugate. Since multiplication is by [conjugate over conjugate], which equals 1, the value is not affected. If a and b are rational numbers, then conjugate of sqrt(b) = sqrt(b) conjugate of a + sqrt(b) = a - sqrt(b), and conjugate of a + ib = a - ib where i is the imaginary square root of -1.
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.
The sum of two irrational is always irrational?
No. In fact, the sum of conjugate irrational numbers is always rational.For example, 2 + sqrt(3) and 2 - sqrt(3) are both irrational, but their sum is 4, which is rational.
What is the graphical relationship between a conjugate number and a complex number?
Graphically, the conjugate of a complex number is its reflection on the real axis.
What is the sum of an rational number and irrational number?
An irrational number.
Is an irrational number plus an irrational number rational?
No. The sum of an irrational number and any other [real] number is irrational.
The sum of a rational number and an irrational number is?
The sum of a rational and irrational number must be an irrational number.
Is 3.56 an irrational number?
No, 3.56 is not an irrational number. 3.56 is rational.
Whether a rational number multiplied by an irrational number gives an irrational number?
rational * irrational = irrational.
Is negative pi rational or irrational?
-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.
What is the relationship between a complex number and its conjugate?
When a complex number is multiplied by its conjugate, the product is a real number and the imaginary number disappears.
