Indices, Standard Form And Surds Worksheet Page 12
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1725.4 Using surds
To rationalise the denominator of a fraction means to get rid of any surds in the denominator.
__
__
__
a
√
b
To rationalise the denominator of
you multiply the fraction by
. This ensures that the fi nal fraction has an
__
__
√
b
√
b
integer as the denominator.
__
__
__
__
√
b
a
a
__
__
__
√
√
√
b
b
b
__
______
a
√
b
__
__
√
b
√
b
__
a
√
b
____
b
__
Example 13
Simplify
12 .
√
___
______
√
12
√
4 3
__
__
____
m
n
mn .
__
__
Use
√
√
√
__
√
4
√
3
4 2.
√
__
2
3
√
__
__
Example 14
Expand and simplify (2
3 )(4
3 ).
√
√
__
__
__
__
__
__
(2
3 )(4
3 ) 8 2
3 4
3
3
3
Multiply out the brackets.
√
√
√
√
√
√
__
8 6
3 3
√
Simplify the expression.
__
11 6
3
√
Exercise 25I
A
Find the value of the integer k.
1
__
__
__
__
__
__
__
__
a
8 k
2
b
18 k
2
c
50 k
2
d
80 k
5
√
√
√
√
√
√
√
√
Simplify
2
___
__
__
__
a
200
b
32
c
20
d
28
√
√
√
√
Solve the equation x
2
30, leaving your answer in surd form.
3
__
A
Expand these expressions. Write your answers in the form a b
c where a, b and c are integers.
4
√
__
__
__
__
__
__
a
3 (2
3 )
b
(
3 1)(2
3 )
c
(
5 1)(2
5 )
√
√
√
√
√
√
__
__
__
__
d
(
7 1)(2
7 )
e
(2
3 )
2
f
(
2 5)
2
√
√
√
√
The area of a square is 40 cm
. Find the length of one side of the square.
2
5
Give your answer as a surd in its simplest form.
__
__
The lengths of the sides of a rectangle are (3
5 ) cm and (3
5 ) cm.
√
√
6
Work out, in their simplifi ed forms:
a
the perimeter of the rectangle
b
the area of the rectangle.
__
The length of the side of a square is (1
2 ) cm. Work out the area of the square.
7
√
__
Give your answer in the form (a b
2 ) cm
2
where a and b are integers.
√
rationalise the denominator
621
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education