Question

Define Surds. Types of surds. Rules of Surds.

Answer 1

The Latin meaning of the word "Surd" is deaf or mute.  In earlier days, Arabian mathematicians called rational numbers and irrational numbers as audible and inaudible. Since surds form are made of irrational numbers, they were referred to as asamm (deaf, dumb) in Arabic language, and were later translated in Latin as surds.

Surd is simply used to refer to a number that does not have a root.

√4, 3√8, √25 have roots as answers.

But √6, 3√2, √20 do not have proper roots.

These number forms are termed as surds.

Answer 2

Surds are the representation number in the form of square root since these numbers cannot be a whole number or a rational number. These numbers cannot be represented as fractions too. For example, consider the value of √2. The value of √2 is said to be recurring. We know the value of  √2 = 1.414213. . . . . . . . . . .but to be accurate we will leave it as a surd. This proves that √2 is a surd.

Types of Surds:

• Simple Surd: When there is only a number present in the root symbol, then it is known as a simple surd. For example

2–√2

  or

5–√5

• Pure Surd: Surds that are irrational are called pure surds. For example

  3–√3

• Similar Surd: When surds have the same common factors, they are known as similar surds.

• Mixed Surds: When numbers can be expressed as a product of rational and irrational numbers, it is known as a mixed surd.

• Compound Surds: The addition or subtraction of two or more surds is known as a complex surd.

• Binomial Surd: when two surds give rise to one single surd, the resultant surd is known as binomial surds.

Rules of Surds:

(i) Addition of surds

Surds typically cannot be added. But we can add equivalent surds.

m√a + n√a = (m + n)√a

For example:

3√5 + 2√5 = 5√5

(ii) Multiplication of surds

We can multiply Surds using the formula below.

√a x √b = √(a x b)

(iii) Rationalizing surds

The denominator can be rationalized by multiplying the numerator and denominator by the single surd present in the denominator.

For example:

√8/√6

By multiplying the denominator by √6, it is possible to rationalize the denominator.