Everything Maths Grade 11
3.2 CHAPTER 3. SURDS
- Expand:
(
√
x−
√
2)(
√
x +
√
2)
- Rationalise the denominator:
10
√
x−^1 x
- Write as a single fraction:
3
2
√
x
+
√
x
- Write in simplest surd form:
(a)
√
72
(b)
√
45 +
√
80
(c)
√
48
√
12
(d)
√
18 ÷
√
72
√
8
(e)
4
(
√
8 ÷
√
2)
(f)
16
(
√
20 ÷
√
12)
- Expand and simplify:
(2 +
√
2)^2
- Expand and simplify:
(2 +
√
2)(1 +
√
8)
- Expand and simplify:
(1 +
√
3)(1 +
√
8 +
√
3)
- Simplify, without useof a calculator:
√
5(
√
45 + 2
√
80)
- Simplify: √
98 x^6 +
√
128 x^6
- Write the followingwith a rational denominator:
√
5 + 2
√
5
- Simplify, without use of a calculator:
√
98 −
√
8
√
50
- Rationalise the denominator:
y− 4
√
y− 2
- Rationalise the denominator:
2 x− 20
√
y−
√
10
- Evaluate without using a calculator:
�
2 −
√
7
2
�^12
×
�
2 +
√
7
2
�^12
- Prove (without the use of a calculator) that:
�
8
3
+ 5
�
5
3
−
�
1
6
=
10
√
15 + 3
√
6
6
