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sqrt(8) = /(8) = sqrt(2 x 4) =>
sqrt(2 x4) = sqrt(2) X sqrt(4) => sqrt(2) X 2 =>
2*sqrt(2)
'2' is a Prime number.
The 'Square Roots' of prime numbers are IRRATIONAL.
sqrt(2) = 1.414213562.... ( to infinity). This makes it irrational .
Hence
2 * 1.414213562.... = 2.828427125..... (Which is also irrational).
NB A rational number multiplied to an irrational number produces an irrational result,.
What else can I help you with?
What is a surd or irrational roots?
Irrational rootsRoots that are irrational are called surds. Irrational numbers are decimals that neither repeat nor terminate. But not all roots are surds. Sqrt(4) is not a surd, because sqrt(4) is + or - 2, which is rational. On the other hand, sqrt(2) is a surd, and that's because the square root of two is irrational.A surd is a number that cannot be changed into a fraction. They go on infinitely without any pattern.
What is an infinite surd?
Infinite surd is a term used in mathematics. The definition of an infinite surd is a never ending irrational number with an exact value that would be left in square root form.
Why was an irrational number called a 'surd' as opposed to an 'irrat'?
The term surd traces back to al-Khwārizmī, who referred to rational and irrational numbers as audible and inaudible, respectively. This later led to the Arabic word "أصم‎" (asamm, meaning "deaf" or "dumb") for irrational number being translated into Latin as "surdus" (meaning "deaf" or "mute").
What is 27 in surd form?
sqrt(27) = sqrt(3 x 9) => sqrt(3) x sqrt(9) => sqrt(3) X 3 => 3*sqrt(3) 3* 1.732050808..... => 5.196152423..... NB 'Sqrt' of prime numbers are IRRATIONAL. Since '3' is a prime number, then its sqrt(3) is irrational at 1.73206080..... NNB The product of a rational number and an irrational number is irrational.
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.
Can you give one example for surd which is not irrational?
It is impossible to have a surd that is not irrational. Surds are defined to be an irrational number (square root of a number).
Are all irrational numbers are surds?
Yes. The definition of a surd is "an irrational number"
In math what is the expression containing irrational roots?
Surd
What is a mathematical expression involving irrational roots?
surd
Are surd's rational?
No because surds are irrational numbers
What is a surd or irrational roots?
Irrational rootsRoots that are irrational are called surds. Irrational numbers are decimals that neither repeat nor terminate. But not all roots are surds. Sqrt(4) is not a surd, because sqrt(4) is + or - 2, which is rational. On the other hand, sqrt(2) is a surd, and that's because the square root of two is irrational.A surd is a number that cannot be changed into a fraction. They go on infinitely without any pattern.
Is root 2 a surd?
Yes the square root of 2 is a surd which is an irrational number that can't be expressed as a fraction.
What does surd mean in maths?
A surd is an irrational number that can't be expressed as a fraction as for example the square root of 2
What is the mathematical definition of surd?
An irrational number such as the square root of 2
What is an infinite surd?
Infinite surd is a term used in mathematics. The definition of an infinite surd is a never ending irrational number with an exact value that would be left in square root form.
Is square root of pi a surd?
Yes. A surd is any irrational number that can be expressed as the root of another number. As pi is a number, although it is a transcendental and hence irrational, the square root of pi is still an irrational number that can be expressed as the square root of another number.
Why pi is not a surd?
'pi' is not a 'surd' because it is not a 'square root' of any number. 'pi' is an IRRATIONAL number. Irrational numbers are those were the decimals go to infinity AND the decinal digits are not in any regular order. pi = 3.141592654.... (recur to infinity and no regular order0. 'pi' in surd form is sqrt(pi) = sqrt(3.141592654....) = 1.772453851..... (which is also irrational). In school/college etc., you are given 'pi = 3.14 , 3.1416 , 22/7' Tese are only APPROXIMATIONS for ease of calculating. 'Super Dupa' computers have calculated 'pi' to at least 50 billion places and still going. NB A decimal number such as 1.33333.... is NOT irrational. It is RATIONAL , because it can be converted to a ration/quotient/fraction. Irrational numbers cannot be converted to an exact value 'ratio/quotient/fraction'. Notice the decimal digits are in a regular order of '3'....
