What is 'Surd"?

Answer 1

In Romanian it means deaf.

Answer 2

Surds
Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. The reason we leave them as surds is because in decimal form they would go on forever and so this is a very clumsy way of writing them.

Addition and Subtraction of Surds
Adding and subtracting surds are simple- however we need the numbers being square rooted (or cube rooted etc) to be the same.

4Ö7 - 2Ö7 = 2Ö7.
5Ö2 + 8Ö2 = 13Ö2

Note: 5Ö2 + 3Ö3 cannot be manipulated because the surds are different (one is Ö2 and one is Ö3).

Multiplication
Ö5 × Ö15 = Ö75 (= 15 × 5)
= Ö25 × Ö3
= 5Ö3.

(1 + Ö3) × (2 - Ö8) [The brackets are expanded as usual]
= 2 - Ö8 + 2Ö3 - Ö24
= 2 - 2Ö2 + 2Ö3 - 2Ö6


Rationalising the Denominator
It is untidy to have a fraction which has a surd denominator. This can be 'tidied up' by multiplying the top and bottom of the fraction by a particular expression. This is known as rationalising the denominator, since surds are irrational numbers and so you are changing the denominator from an irrational to a rational number.

Example
Rationalise the denominator of:
a) 1
Ö2 .

b) 1 + 2
1 - Ö2

a) Multiply the top and bottom of the fraction by Ö2. The top will become Ö2 and the bottom will become 2 (Ö2 times Ö2 = 2).

b) In situations like this, look at the bottom of the fraction (the denominator) and change the sign (in this case change the plus into minus). Now multiply the top and bottom of the fraction by this.

Therefore:

1 + 2 = (1 + 2)(1 + Ö2) = 1 + Ö2 + 2 + 2Ö2 = 3 + 3Ö2
1 - Ö2 (1 - Ö2)(1 + Ö2) 1 + Ö2 - Ö2 - 2
- 1



= -3(1 + Ö2)


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Answer 3

The answer from "finalmoksha" is most correct. A surd is a square root, cube root, and so on which does not come out as a whole number or rational fraction. I have also seen "mixed surd" for an expression which includes a surd.

It is interesting that it means "deaf" in Romanian, and that the French word for "deaf" is "sourd". These both obviously come from the Latin "surdus" meaning "deaf". Early mathematical writers, writing in Latin of course, called these unresolved roots "deaf numbers" because they behaved as if they didn't hear you asking them to please simplify into something tidier. The English word must have been invented when the Latin texts were translated later.

Answer 4

Have u studied rational numbers????? u may know that there are fractions like a/b and if the b is a square root. then the b is known as surd. to solve the equation we need to remove surds by multipying the surd on both sides. hope u understood, coz it's hard to explain in this manner. good luck!

Answer 5

Any number written in the form of

nth ROOT of x

is called a surd.

ROOT above represents the math symbol used for a root like the square root symbol.

Surd is also an old-fashioned, outdated term in ancient math books meaning an irrational number.

A surd is also defined as a sum containing one or more irrational numbers.


What are such things to me
whose life is full of indices and surds?
x squared plus seven x plus fifty three
equals eleven thirds!

Edgar Allen Poe
  

Answer 6

In India Surd means Sardarjee however in maths it is an irrational number that is not rational of the form p/q for example sqrt(2)

Answer 7

A surd is a number or quantity that cannot be expressed as the ratio of two integers.

Answer 8

a surd is a non recurring continuous decimal....root of 2

Answer 9

well a "Sikh" or Sardar ji is called a Surd aswell.

Answer 10

An unresolved mathematical expression of an nth root.