Mathematics FET Grade 11 Term 1: Exponents Surds

1. EXPONENTIAL SURDS
SURDS
Irrational
Decimals

2. After the lesson you must be able
to
 Identify common factors.
 Add common factors.
 Apply exponential laws on surds.
LEARNING OUTCOMES
A+2A= A(1+2)
 2C+C-D= 3C-D
 SQROOT 2 = 2^(1/2)


3. COMMON FACTORS
NAME COMMON THINGS BETWEEN THE 2 GROUPS.

Group A

Group B

4. COMMON FACTORS
Like the title says “common” factor Meaning
this that are the same.
 The look alike. In Surds we add those surds
that look alike.
 E.g. root A + root A = 2root A
 This is because the variables under our are
both a thus there are common so they can
be added/subtracted together.


5. COMMON FACTORS



This brings us to the
next point.
Products or quotients
of equations DO NOT
REQUIRE YOU TO
FIND COMMON
FACTORS!!!
Root A * Root A


1.
2.
3.
Class work
Try the following
Root 5 + 3root 5
Root 2 - 4root 2
2root a + 7root a – root
b

6. SURDS
Surds are irrational roots.
 Remember we said irrational roots are those
that are not perfect so their nature is always
a decimal number. 0.84682492
 What’s the root of this tree?


7. EXPONENTIAL LAWS




Fundamental laws when
working with surds are as
follows:
a to the power of half =
square root of a
a to the power of 1/5 = fifth
root of 5
Therefore this tells that
any exponent that’s a
fraction is a root, and the
denominator in the fraction
informs you the nature of
that root.


1)
2)
3)
4)
5)
Now that you have an
idea
try the
following.
Convert from surd form to
exponential form.
Sixth root of a
Square root of 3
Cubed root of 27
Tenth root of a thousand
Hundredth root of a
hundred

8. COMMON FACTORS



The same.
You can add or subtract
common factors.
You can take out a
common factor in an
expression. NB: ONLY
WHEN YOU ADD AND
SUBTRACT.
SUMMARY
SURDS



They can be added or
subtracted only when they
are common.
You use exponential laws
to solve them.
They correspond with
exponential fractions.