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Random squared number

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List of random square number between 1 and 36

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d times f

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square root of the selected square number d.

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Random number between 1 and 12 except 4 and 9.

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Random number between 2 and 12

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Random squared number but not the same number as a.

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a times b

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square root of the squared numbers

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List of squared numbers from 1 to 144

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Surd

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Not a surd

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$\\sqrt{\\var{square}}$

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$\\sqrt{\\var{h}}$

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$^3\\sqrt{\\var{cube}}$

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$\\sqrt{\\var{j}}$

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$\\sqrt{\\var{k}}$

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

\n

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$4\\sqrt3$

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$2\\sqrt{11}$

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$2\\sqrt{14}$

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$4\\sqrt{2}$

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i) $\\sqrt{48}$

", "

ii) $\\sqrt{32}$

", "

iii) $\\sqrt{56}$

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iv) $\\sqrt{44}$

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Match each surd with the equivalent simplification.

\n

[[0]]

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Simplify the following surds:

\n

$\\displaystyle\\sqrt{\\var{c}}$ = [[0]]$\\displaystyle\\sqrt{\\var{b}}$

\n

$\\displaystyle\\sqrt{\\var{g}}$ = [[1]]$\\displaystyle\\sqrt{\\var{f}}$

\n

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This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

"}, "name": "Katy's copy of Surds simplification", "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.

a)

\n

$\\sqrt{\\var{square}}$ 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.

\n

$\\sqrt{\\var{h}}$, $\\sqrt{\\var{j}}$ 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.

\n

\n

\n

b)

\n

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

\n

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

\n

i)

\n

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

\n

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

\n

ii)

\n

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

\n

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

\n

iii)

\n

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

\n

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

\n

iv)

\n

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

\n

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

\n

\n

c)

\n

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

\n

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

\n

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

\n

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

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