LHS Surds simplification

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Harry Flynn 6 years, 6 months ago

Created this as a copy of Surds simplification.

Name	Status	Author	Last Modified
Surds simplification	Ready to use	Lauren Richards	20/11/2019 14:43
Inbbavathie's copy of Surds simplification	draft	Inbbavathie Ravi	24/07/2017 03:48
LHS Surds simplification	draft	Harry Flynn	27/09/2018 10:33
Simon's copy of Surds simplification	draft	Simon Thomas	06/06/2019 10:08
Katy's copy of Surds simplification	draft	Katy Dobson	03/09/2019 08:29
Vereinfachung von Wurzelausdrücken	Ready to use	Ulrich Görtz	26/11/2020 10:28

There are 17 other versions that do you not have access to.

Question statement

Surds are square roots that cannot be simplified to a whole number. They have a decimal equivalent but their decimal representations are never-ending. Therefore, it is often easier to leave surds as they are in algebraic calculations.

Give any introductory information the student needs.

			Name	Type	Generated Value

aoptions	list	List of 11 items
b	integer	10
a	integer	49
c	integer	490
sqrta	number	7
doptions	list	List of 12 items
sqrtd	number	1
d	integer	1
f	integer	6
g	integer	6
square	integer	25
cube	integer	27
h	integer	7
j	integer	6
k	integer	11
root	number	3

Automatically regenerate variables?

Name

Data type

Value

(numbers)

Description

List of random square number between 1 and 36

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Match choices with answers
Part b) Gap-fill
1. Gap Match choices with answers
  Add
Part c) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Match choices with answers

Ask the student a question, and give any hints about how they should answer this part.

For the following examples, tick the correct box to determine whether or not they are a surd.

Minimum marks

Maximum marks

(no maximum)

Show correct answer on reveal?

Show score feedback icon?

Advanced settings

Minimum answers

Maximum answers

(no maximum)

What to do if wrong number of answers selected:

Selection type

Layout

Show choice feedback state?

$\sqrt{\var{square}}$
$\sqrt{\var{h}}$
$^3\sqrt{\var{cube}}$
$\sqrt{\var{j}}$
$\sqrt{\var{k}}$

Surd
Not a surd

For each combination of answer and choice, specify the number of marks to add or subtract when the student picks it.

	Surd	Not a surd
$\sqrt{\var{square}}$
$\sqrt{\var{h}}$
$^3\sqrt{\var{cube}}$
$\sqrt{\var{j}}$
$\sqrt{\var{k}}$

Advice

a)

$\sqrt{\var{square}}$ and $\sqrt[3]{\var{cube}}$ are not surds, as they can be simplified to whole integers: $\simplify{{sqrt(square)}}$ and $\var{root}$ respectively. They are roots, but not surds. All surds are roots but not all roots are surds.

$\sqrt{\var{h}}$ , $\sqrt{\var{j}}$ and $\sqrt{\var{k}}$ are surds, as they cannot be simplified to a whole integer. There is no number, $b$ , such that $b^2=\var{h}, \var{j}$ or $\var{k}$ . Therefore, $\sqrt{\var{h}}$ , $\sqrt{\var{j}}$ and $\sqrt{\var{k}}$ are both roots and surds.

b)

The rule that should be used is $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$ .

We need to try to find a square number that divides $ab$ and rewrite this as $\sqrt{b^2}\times\sqrt{a}$ .

$\sqrt{48}$ = $\sqrt{16}\times\sqrt3$

$\sqrt{16}$ simplifies down to $4$ so the final answer is: $4\sqrt3$ .

ii)

$\sqrt{56}$ = $\sqrt{4}\times\sqrt{14}$

$\sqrt4$ simplifies down to $2$ so the final answer is: $2\sqrt{14}$ .

iii)

$\sqrt{32}$ = $\sqrt{16}\times\sqrt{2}$

$\sqrt{16}$ simplifies down to $4$ so the final answer is: $4\sqrt2$ .

iv)

$\sqrt{44}$ = $\sqrt{4}\times\sqrt{11}$

$\sqrt4$ simplifies down to $2$ so the final answer is: $2\sqrt{11}$ .

c)

This question requires you to notice that $\sqrt{\var{a}}$ and $\sqrt{\var{d}}$ are squared numbers and can be simplified to integers.

$\sqrt{\var{a}}$ = $\var{sqrta}$ such that:

i) $\sqrt{\var{c}}$ = $\sqrt{\var{a}}$ x $\sqrt{\var{b}}$ = $\var{sqrta}\sqrt{\var{b}}$ and

ii) $\sqrt{\var{g}}$ = $\sqrt{\var{d}}$ x $\sqrt{\var{f}}$ = $\var{sqrtd}\sqrt{\var{f}}$ .

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Match choices with answers
Match choices with answers		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Match choices with answers
Match choices with answers		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

LHS Quiz 1 by Harry Flynn in Numeracy.
Maths for Chemists Quiz 1 by Harry Flynn in Numeracy.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Harry Flynn 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Match choices with answers

Advanced settings

a)

b)

c)

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Error

LHS Surds simplification

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Harry Flynn 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Match choices with answers

Advanced settings

a)

b)

c)

Generated value: `list`