LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SURDS

__SURDS -__

**Around 820 AD a Persian guy name Al-Khwarizmi called irrational numbers
“inaudible”….. this was later translated to the Latin SURDS (“Deaf” or “mute”).
In fact "Surd" used to be considered by another name
for "Irrational", but it is now used for a root that
is irrational.**

**Let, ‘x’ be a rational number and ‘n’ be a positive integer such that ^{n}√x
is irrational, then ^{n}√x is
called a ‘Surd’ or a ‘Radical’ of order n.
**

**There are some important notes are given below - ^{3}√11**

**1) ^{n}√x is a surd only
when ‘x’ is rational and ^{n}√x is irrational.**

**2) When ‘x’ is irrational or ^{n}√x is rational, then ^{n}√x is not a Surd**

__Example.1)__ ^{3}√5, ^{5}√11, ^{7}√8, and ^{9}√14 are surds of order 3, 5, 7, and 9 respectively because 5, 11, 8, and 14
cannot be simplified further

__Example.2)__ ^{3}√64 is not a
surd, since ^{3}√64 = ^{3}√4^{3} = 4,
is not a surd, since ^{3}√64, which is rational because 64 can
be simplified ^{3}√64 = ^{3}√4^{3} = 4.

__Example.3)__ √π is not a surd,
because π is rational.