Surds simplification

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Christian Lawson-Perfect	said	Ready to use	7 years, 8 months ago
Lauren Richards	said	Needs to be tested	7 years, 9 months ago
Chris Graham	said	Has some problems	7 years, 9 months ago

History

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

I'd like a description of how you decide if a root is a surd or not, like " $\sqrt{a}$ is a surd because there is no whole number $b$ such that $b^2 = a$ ".

Similarly for part b), describe the strategy: find a square number which divides $a$ , and rewrite as $\sqrt{b^2} \times \sqrt{c}$ . (Or, do what I did and multiply out the $a\sqrt{b}$ forms - much easier!)

Otherwise, this looks good.

Restore this checkpoint

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Bradley Bush commented 7 years, 9 months ago

This question was really hard to criticise, I only came up with a few pedantic points.

It might have been nice to see more random variables in part a) and maybe part b) so the student can repeat this question for practice.

You may have missed a fullstop in the advice for part bi), and I'm not sure you need fullstops after each equation in the advice to part b, maybe using a comma instead would be better?

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Lauren Richards commented 7 years, 9 months ago

I have enacted the changes you requested.

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Lauren Richards 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Chris Graham 7 years, 9 months ago

Gave some feedback: Has some problems

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Chris Graham commented 7 years, 9 months ago

Where you are using \sqrt, you should have braces around the argument \sqrt{...}. Note the difference: $\sqrt100$ and $\sqrt{100}$ .

Also the nth root can be written \sqrt[n]{...}, e.g. \sqrt[3]{100}, $\sqrt[3]{100}$ .

If this is the first question on surds when we put questions together, then I think an example surd would be beneficial in the statement.

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Lauren Richards commented 7 years, 9 months ago

I have changed part b) of the original question and have made the rationalising the denominator sections of this original question into a different question purely on that.

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Lauren Richards 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Christian Lawson-Perfect 7 years, 9 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect commented 7 years, 9 months ago

The prompt for part b is hopelessly generic! "Match each product with the equivalent surd" might do, but that's not quite right either. Also think about how the numbers are laid out - would it be better to put the products down the side and collected surds on top? As it is, I can rule out a few combinations without thinking, like $\sqrt{44}$ is obviously not equal to $\sqrt{30}$ .

Part c: I would repeat $\sqrt{n} =$ before the gap-fill. As stated, how is " $\sqrt{300} = \sqrt{100} \times \sqrt{3}$ , so $\sqrt{300} = ?? \times \sqrt{3}$ " different to $\sqrt{100} = ??$ ". Maybe just $\sqrt{300} = \text{[gapfill]} \times \sqrt{3}$ would do.

Part d: for "simplify" to make sense here, I think you need to give the hint that they can be simplified to whole numbers.

Part e: instead of [1] and [2], write $a$ and $b$ . I got $\frac{\sqrt{6}}{\sqrt{3}}$ , which it expected me to write as $\frac{\sqrt{18}}{3}$ . I'd write that as just $\sqrt{2}$ . Can you set it up so there's only one way of writing it? Making sure the top and bottom of the original fraction are coprime might do it.

Part f: I had to reduce the fraction - you should say that in the prompt. "Rationalise the denominator of this expression and reduce to lowest terms".

In parts g, h and i, the big expression is REALLY big - have you formatted it as a header? I don't think you need the "= ?" bit, or "and select the correct answer from the list of options".

None of the parts of this question really lead on from each other - you could split this into several smaller questions.
Advice
Some numbers not in LaTeX in part a. "Roots are necessary but not sufficient conditions for surds" isn't completely clear - I'd say "all surds are roots, but not all roots are surds".

Part e: this might be incredibly pedantic, but does "the denominator is $\sqrt{6}$ " sound better than "\sqrt{6} is the denominator" to you?

A few sentence of a similar form to "This gives the final answer as:"; I would say "So the final answer is:".

Some wordy explanation of what's happening at each step, or a description of the plan of attack, in part f wouldn't go amiss.

Part g: It's not true that you can't multiply by those things, it just doesn't help. Get someone else to read that paragraph and have a go at rewriting it: it's a bit long and easy to get lost in. There's an unhelpful "simply" in there, too.

I have a few problems with this sentence: "To be able to do a question like $\frac{2}{\sqrt2+\sqrt8}+\frac{1}{3}$ which requires you to add fractions, you need to have the same denominator."

$\frac{2}{\sqrt2+\sqrt8}+\frac{1}{3}$ isn't a question, it's an expression.

"you need to have the same denominator" isn't a complete phrase - the same as what?

Try:

To add $\frac{2}{\sqrt2+\sqrt8}$ to $\frac{1}{3}$ , you must put write both terms with the same denominator."

Likewise, "the question is now $\frac{2}{3\sqrt2}+\frac{1}{3}$ " isn't right. You could say "the expression is now ...".

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Christian Lawson-Perfect 7 years, 9 months ago

Saved a checkpoint:

I've reworded the statement slightly.

Restore this checkpoint

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Lauren Richards 7 years, 9 months ago

Gave some feedback: Needs to be tested

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Lauren Richards 7 years, 9 months ago

Created this.

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 12 items
b	integer	10
a	integer	49
c	integer	490
sqrta	number	7
doptions	list	List of 12 items
sqrtd	number	9
d	integer	81
f	integer	11
g	integer	891
square	integer	81
cube	integer	27
h	integer	7
j	integer	2
k	integer	12
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`

[ 1, 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

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Taxonomy: Kind of activity

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Checkpoint description

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Bradley Bush commented 7 years, 9 months ago

Lauren Richards commented 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Lauren Richards commented 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect commented 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards 7 years, 9 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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Surds simplification

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Bradley Bush commented 7 years, 9 months ago

Lauren Richards commented 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Chris Graham 7 years, 9 months ago

Chris Graham commented 7 years, 9 months ago

Lauren Richards commented 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Christian Lawson-Perfect commented 7 years, 9 months ago

Christian Lawson-Perfect 7 years, 9 months ago

Lauren Richards 7 years, 9 months ago

Lauren Richards 7 years, 9 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`