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Lets say I have this: $ 2\dfrac{2}{3}\sqrt{2\dfrac{2}{3}}$ and I want to make this more simple, are my following steps correct?

$ 2\dfrac{2}{3}\sqrt{2\dfrac{2}{3}} = 2\dfrac{2}{3}\sqrt{\dfrac{24}{9}}$ = $2\dfrac{2}{3} . \dfrac{1}{3} . 2\sqrt{6} = \dfrac{16}{9} \sqrt{6}$

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    Thank you, it indeed means two-and-two-thirds2012-10-13

2 Answers 2

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$2\frac{2}{3}\sqrt{2\frac{2}{3}}=\frac{8}{3}\sqrt{\frac{8}{3}}=\frac{16}{3}\sqrt{\frac{2}{3}}=\frac{16}{9}\sqrt{6}$

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The second step is wrong, since $2 \cdot 2 \cdot 3 = 12$, not $24$. I think you should note that $\sqrt{2 \cdot 2} = 2$.

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    It's pretty common fraction arithmetic notation before students learn basic algebra, at least in my country.2012-10-13