Vereinfachung von Wurzelausdrücken

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From users who are members of Lineare Algebra 1 :

Ulrich Görtz

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4 years, 5 months ago

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Ulrich Görtz 4 years, 5 months ago

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Ulrich Görtz 4 years, 5 months ago

Gave some feedback: Ready to use

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Ulrich Görtz 4 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

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Question statement

Einige einfache Aufgaben zur Vereinfachung von Ausdrücken mit Quadratzahlen.

Give any introductory information the student needs.

			Name	Type	Generated Value

aoptions	list	List of 12 items
b	integer	10
a	integer	1
c	integer	10
sqrta	number	1
doptions	list	List of 12 items
sqrtd	number	2
d	integer	4
f	integer	10
g	integer	40
square	integer	49
cube	integer	64
h	integer	3
j	integer	5
k	integer	12
root	number	4

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 ]

→ Used by:

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.

Welche der folgenden Zahlen sind rational (lassen sich als Bruchzahl darstellen), welche irrational (lassen sich nicht als Bruchzahl darstellen)?

Minimum marks

Maximum marks

(no maximum)

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Advanced settings

Minimum answers

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(no maximum)

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

Irrational
Rational

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

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

Advice

a)

$\sqrt{\var{square}}$ und $\sqrt[3]{\var{cube}}$ sind rational, und zwar sogar ganze Zahlen: $\simplify{{sqrt(square)}}$ bzw. $\var{root}$ .

$\sqrt{\var{h}}$ , $\sqrt{\var{j}}$ und $\sqrt{\var{k}}$ sind irrational. Es gibt keine ganzen Zahlen $a, b$ , $b\ne 0$ so dass $\left(\frac ab\right)^2=\var{h}$ (oder $= \var{j}$ oder $=\var{k}$ ). Eine Möglichkeit, das zu sehen, ist, den Satz über die eindeutige Primzaktorzerlegung von ganzen Zahlen zu benutzen. Wenn $\left(\frac ab\right)^2=\var{h}$ gilt, also $a^2 = hb^2$ , dann kommt in der eindeutigen Primfaktorzerlegung der linken Seite jede Primzahl mit einem geraden Exponenten vor; auf der rechten Seite ist das nicht der Fall.

b)

Benutzen SIe, dass $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$ .

Wir suchen nach einer Quadratzahl, die $ab$ teilt, und schreiben das als $\sqrt{b^2}\times\sqrt{a}$ .

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

$\sqrt{16}$ ist $4$ , also ist die Antwort: $4\sqrt3$ .

ii)

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

$\sqrt4$ ist $2$ , also erhalten wir: $2\sqrt{14}$ .

iii)

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

$\sqrt{16}$ ist $4$ , wir bekommen also: $4\sqrt2$ .

iv)

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

$\sqrt4$ ist $2$ , also erhalten wir: $2\sqrt{11}$ .

c)

Beachten Sie, dass $\sqrt{\var{a}}$ und $\sqrt{\var{d}}$ Wurzeln aus Quadratzahlen sind.

$\sqrt{\var{a}}$ = $\var{sqrta}$ , folglich:

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.

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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 exam:

Einfache Gleichungen by Ulrich Görtz in Lineare Algebra 1.

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Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 years, 6 months ago

Error in variable testing condition

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Generated value: `list`

Parts

Match choices with answers

Advanced settings

a)

b)

c)

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Vereinfachung von Wurzelausdrücken

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 years, 5 months ago

Ulrich Görtz 4 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`