Surds: Simplifying Expressions 2a

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Created this as a copy of Surds: Simplifying Expressions 2b.

Name	Status	Author	Last Modified
Surds: Simplifying Expressions 1a	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 1b	Ready to use	Ben McGovern	15/08/2023 15:04
Surds: Simplifying Expressions 2b	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 2a	Ready to use	Ben McGovern	15/08/2023 15:49
Surds: Simplifying Expressions 3a	Ready to use	Ben McGovern	15/08/2023 15:31
Surds: Simplifying Expressions 3b	Ready to use	Ben McGovern	15/08/2023 15:14
Surds: Simplifying Expressions 4a	Ready to use	Ben McGovern	15/08/2023 15:29
Surds: Simplifying Expressions 4b	Ready to use	Ben McGovern	15/08/2023 15:26
Surds: Simplifying Expressions 4c	Ready to use	Ben McGovern	15/08/2023 15:50
Surds: Simplifying Expressions 5a - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 15:55
Surds: Simplifying Expressions 5b - Rationalising the Denominator	Ready to use	Ben McGovern	15/08/2023 16:07
Surds: Simplifying Expressions 6 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Surds: Simplifying Expressions 7 - Rationalising the Denominator	Ready to use	Ben McGovern	21/09/2022 16:31
Quadratics: Using the Quadratic Formula	Ready to use	Ben McGovern	14/09/2022 16:14
Quadratics: Factorisation 1	Ready to use	Ben McGovern	14/08/2023 15:01
Quadratics: Factorisation 2	Ready to use	Ben McGovern	14/08/2023 15:14
Quadratics: Completing the Square 1	Ready to use	Ben McGovern	14/08/2023 14:59
Quadratics: Completing the Square 2	Ready to use	Ben McGovern	14/09/2022 16:03
Quadratics: Interpreting the Discriminant	Ready to use	Ben McGovern	14/09/2022 16:08
Quadratics: Factorisation 3 - Difference of 2 squares	Ready to use	Ben McGovern	14/08/2023 15:33
Indices: Simplification 1a	Ready to use	Ben McGovern	26/06/2023 12:12
Indices: Simplification 1b	Ready to use	Ben McGovern	26/06/2023 14:31
Indices: Simplification 1c	Ready to use	Ben McGovern	26/06/2023 14:30
Indices: Simplification 2a	Ready to use	Ben McGovern	26/06/2023 14:33
Indices: Simplification 2b	Ready to use	Ben McGovern	26/06/2023 14:36
Indices: Simplification 3a	Ready to use	Ben McGovern	26/06/2023 14:37
Indices: Simplification 3b	Ready to use	Ben McGovern	26/06/2023 14:40
Indices: Change of Notation 1	Ready to use	Ben McGovern	15/08/2023 11:43
Indices: Change of Notation 2	Ready to use	Ben McGovern	15/08/2023 11:51
Indices: Change of Notation 3	Ready to use	Ben McGovern	15/08/2023 11:54
Solve Quadratics - Factorisation 1	Ready to use	Ruth Hand	14/08/2023 15:44
Quadratics: Solving a Quadratic Equation	Ready to use	Ben McGovern	09/12/2022 16:45
Quadratics: Solving by Factorisation	Ready to use	Ben McGovern	14/09/2022 16:25
AD2 Quadratics - solve	Ready to use	Megan Oliver	09/04/2024 15:13
AD5 Difference of two squares	Ready to use	Megan Oliver	09/04/2024 15:14
AA2 Indices - divide	Ready to use	Andrew Neate	09/04/2024 15:00
AA4 Indices - Fractional 2	Ready to use	Andrew Neate	09/04/2024 15:01
AA3 Indices - Fractional 1	Ready to use	Andrew Neate	09/04/2024 15:01
AA1 Indices - times	Ready to use	Andrew Neate	28/03/2024 13:17
Calculation with indices - times	Ready to use	Will Morgan	26/06/2024 11:53
Calculation with Indices - divide	Ready to use	Will Morgan	26/06/2024 12:07

There are 209 other versions that do you not have access to.

Question statement

Rewrite the following expression in the form $a\sqrt{b}$ :

$\simplify{sqrt({b1^2*c})+{sgn}*sqrt({b2^2*c})}$

Give any introductory information the student needs.

			Name	Type	Generated Value

b1	integer	8
c	integer	7
b2	integer	6
sgn	integer	1

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Value

xxxxxxxxxx
 
random(2..8)

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Generated value: `integer`

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Advice

To write $\simplify{sqrt({b1^2*c})+{sgn}*sqrt({b2^2*c})}$ in the form $a\sqrt{b}$ we need to be able to rewrite $\simplify{sqrt({b1^2*c})}$ and $\simplify{sqrt({b2^2*c})}$ such that both have the same surd as a common factor.

We see that

$\sqrt{\var{b1^2*c}} = \sqrt{\var{b1^2}\times\var{c}}\,, \qquad \sqrt{\var{b2^2*c}} = \sqrt{\var{b2^2}\times\var{c}}.$

If we then apply the rule $\sqrt{ab} = \sqrt{a} \sqrt{b}$ :

$\begin{split} \sqrt{\var{b1^2*c}} &\,= \sqrt{\var{b1^2}} \times \sqrt{\var{c}}\,, \qquad \sqrt{\var{b2^2*c}} &\,= \sqrt{\var{b2^2}} \times \sqrt{\var{c}} \\ &\,= \var{b1} \sqrt{\var{c}} &\,= \var{b2} \sqrt{\var{c}} \end{split}$

Therefore,

$\begin{split} \simplify{sqrt({b1^2*c})+{sgn}*sqrt({b2^2*c})} &\,= \simplify[!collectNumbers]{{b1}sqrt({c}) + {sgn*b2}sqrt({c})} \\ &\,= \simplify{{b1+sgn*b2}sqrt({c})}. \end{split}$

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This question is used in the following exams:

Surds Quiz by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Surds by Ben McGovern in MASH Bath: Moodle quizzes and TS.
All the good stuff by Chris Templet in Chris's workspace.
extension quiz by Billy Woods in Billy's workspace.
surds by Dean Ang in Dean's workspace.
EC1602 NUMBAS 2 by samira Al-Moustafa in samira's workspace.

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Ben McGovern 2 years, 7 months ago

Ben McGovern 3 years, 9 months ago

Ben McGovern 4 years, 10 months ago

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Surds: Simplifying Expressions 2a

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 2 years, 7 months ago

Ben McGovern 3 years, 9 months ago

Ben McGovern 4 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`