<s>[INST] How to simplify $42\sqrt{45} \over 7\sqrt{35}$? The problem is $$42\sqrt{45} \over 7\sqrt{35}$$ HELP! My daughter's math sheet shows how to reduce the squareroots, but the examples all use the same square-root; the problems show two different numbers square-rooted. Can you please help work this problem so I know how to help her with this assignment?
Thanks!
 [/INST] $$\frac{42\sqrt{45}}{7\sqrt{35}} = \frac{6\times 7\sqrt{9\times 5}}{7\sqrt{7\times 5}} $$ 
$$ = \frac{6\sqrt 9 \times \sqrt 5}{\sqrt 7 \times \sqrt 5} = \frac{6\times \sqrt 9}{\sqrt 7}$$
$$= \frac{6 \times 3}{\sqrt 7} \times \frac{\sqrt 7}{\sqrt 7} = \frac{18\sqrt 7}{ 7}$$ 
Cancel common factors, then multiply denominator to clear the square root.
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