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#### Checkpoint description

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Published this.

#### Christian Lawson-Perfect7 years, 1 month ago

Gave some feedback: Ready to use

#### Christian Lawson-Perfect7 years, 1 month 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.

#### Bradley Bush commented 7 years, 1 month 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?

#### Lauren Richards commented 7 years, 1 month ago

I have enacted the changes you requested.

#### Lauren Richards7 years, 1 month ago

Gave some feedback: Needs to be tested

#### Chris Graham7 years, 1 month ago

Gave some feedback: Has some problems

#### Chris Graham commented 7 years, 1 month 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.

#### Lauren Richards commented 7 years, 1 month 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.

#### Lauren Richards7 years, 1 month ago

Gave some feedback: Needs to be tested

#### Christian Lawson-Perfect7 years, 1 month ago

Gave some feedback: Has some problems

#### Christian Lawson-Perfect commented 7 years, 1 month 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 gh 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.

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 ...".

#### Christian Lawson-Perfect7 years, 1 month ago

Saved a checkpoint:

I've reworded the statement slightly.

#### Lauren Richards7 years, 1 month ago

Gave some feedback: Needs to be tested

#### Lauren Richards7 years, 1 month ago

Created this.
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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