Surds: Simplifying & Rationalising (Grade 11) — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 11 · Exponents and Surds

Surds: Simplifying & Rationalising (Grade 11)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 34

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Simplify √72
(2)
6√2✓✓ (2)
2
Simplify √50
(2)
5√2✓✓ (2)
3
Simplify √98
(2)
7√2✓✓ (2)
4
Simplify √12 + √27
(2)
2√3 + 3√3 = 5√3✓✓ (2)
5
Simplify 3√2 + √50
(2)
8√2✓✓ (2)
6
Simplify √5 × √20
(2)
√100 = 10✓✓ (2)
7
Expand (√3 + 2)(√3 − 5)
(3)
−7 − 3√3✓✓✓ (3)
8
Rationalise 6/(√3)
(2)
2√3✓✓ (2)
9
Rationalise 1/(√5)
(2)
(√5)/5✓✓ (2)
10
Rationalise 4/(1 + √2)
(3)
−4 + 4√2✓✓✓ (3)
11
Solve for x: √(x − 4) = 5
(3)
x − 4 = 25 ✓; x = 29 ✓; check: √25 = 5 ✓(3)
12
Solve for x: 2√x + 1 = 9
(3)
2√x = 8 ✓; √x = 4 ✓; x = 16 ✓(3)
13
Solve for x: √(x + 6) = x, and reject any invalid answer with a reason.
(4)
x + 6 = x² ✓; x² − x − 6 = 0, so (x − 3)(x + 2) = 0 ✓; x = 3 or x = −2 ✓; x = −2 is rejected because √4 = 2, not −2, so x = 3 ✓(4)
14
Explain why √(x + 1) = −3 has no solution.
(2)
A square root is never negative ✓; so no value of x can make the left side equal −3 ✓(2)

TOTAL: 34 marks