Everything Maths Grade 11

3.2 CHAPTER 3. SURDS

or similarly

c

√

a−

√

b

=

√

a +

√

b

√

a +

√

b

×

c

√

a−

√

b

(3.10)

=

c

√

a + c

√

b

a− b

Example 4: Rationalising the Denominator

QUESTION

Rationalise the denominator of:^5 x√−x^16

SOLUTION

Step 1 : Rationalise the denominator

To get rid of

√

x in the denominator, youcan multiply it out by another

√

x. This

rationalises the surd in the denominator. Note that

√x

√x= 1, thus the equation

becomes rationalised bymultiplying by 1 (although its’ value stays the same).

5 x− 16

√

x

×

√

x

√

x

Step 2 : Multiply out the numerators and denominators

The surd is expressed inthe numerator which isthe preferred way to write ex-

pressions. (That’s why denominators get rationalised.)

5 x

√

x− 16

√

x

x

=

(

√

x)(5x− 16)

x

Example 5: Rationalising the Denominator

QUESTION

Rationalise the following:√^5 xy−−^1610

SOLUTION

Step 1 : Rationalise the denominator